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mathematics
precalculus 1st

Precalculus 1st Edition Jay Abramson - Solutions

For the following exercises, graph y = 3 √— x on the given viewing window. Determine the corresponding range for each viewing window. Show each graph. [−1,000, 1,000]
For the following exercises, let F(x) = (x + 1)5 , f(x) = x5 , and g(x) = x + 1. True or False: (f ∘ g )(x) = F(x).
For the following exercises, let F(x) = (x + 1)5 , f(x) = x5 , and g(x) = x + 1. True or False: ( g ∘ f)(x) = F(x).
For the following exercises, graph y = 3√— x on the given viewing window. Determine the corresponding range for each viewing window. Show each graph. [−0.001, 0.001]
For the following exercises, use f(x) = x3 + 1 and g(x) = 3 √x − 1.Let f(x) =1/x.a. Find (f ∘ f)(x).b. Is (f ∘ f)(x) for any function f the same result as the answer to part (a) for any function? Explain.
For the following exercises, graph y = √ — x on the given viewing window. Determine the corresponding range for each viewing window. Show each graph. [0, 10,000]
For the following exercises, use f(x) = x3 + 1 and g(x) = 3 √x − 1.What is the domain of(f ∘ g)(x)?
For the following exercises, graph y = √ — x on the given viewing window. Determine the corresponding range for each viewing window. Show each graph. [0, 100]
For the following exercises, use f(x) = x3 + 1 and g(x) = 3 √x − 1.What is the domain of (g ∘ f)(x)?
For the following exercises, graph y = √ — x on the given viewing window. Determine the corresponding range for each viewing window. Show each graph. [0, 0.01]
For the following exercises, use the graph in Figure 32 to sketch the given transformations. g(x) = f(x − 2) 404 Figure 32 $10
For the following exercises, use f(x) = x3 + 1 and g(x) = 3 √x − 1.Find (f ∘ g)(2) and (g ∘ f)(2).
For the following exercises, use the graph in Figure 32 to sketch the given transformations.g(x) = f (x + 1) I -10-8-6-4- y 10 8 6+ 2 -8+ -10- D [I 2 4 6 8 10 Figure 32 X
For the following exercises, graph y = x3 on the given viewing window. Determine the corresponding range for each viewing window. Show each graph. [−100, 100]
For the following exercises, use f(x) = x3 + 1 and g(x) = 3 √x − 1. Find (f ∘ g)(x) and (g ∘ f)(x). Compare the two answers.
For the following exercises, use the graph in Figure 32 to sketch the given transformations. g(x) = −f(x) ம் 64 + y Figure 32 பம் x
For the following exercises, use a graphing utility to determine whether each function is one-to-one.If f(1) = 4, find f−1 (4).
For the following exercises, graph y = x3 on the given viewing window. Determine the corresponding range for each viewing window. Show each graph. [−10, 10]
For the following exercises, use the graph in Figure 32 to sketch the given transformations.g(x) = f(x) − 2 10 B quand 404 Sig +6+ obje figure -10- Figure 32 II 810 x
For the following exercises, use the functions f(x) = 2x2 + 1 and g(x) = 3x + 5 to evaluate or find the composite function as indicated.(g ∘ g)(x)
For the following exercises, use a graphing utility to determine whether each function is one-to-one.If f(5) = 2, find f−1 (2).
For the following exercises, graph y = x3 on the given viewing window. Determine the corresponding range for each viewing window. Show each graph. [−0.1, 0.1]
For the following exercises, use the functions f(x) = 2x2 + 1 and g(x) = 3x + 5 to evaluate or find the composite function as indicated.g(f( − 3))
For the following exercises, use a graphing utility to determine whether each function is one-to-one.f(x) = −3x2 + x
For the following exercises, graph y = x2 on the given viewing window. Determine the corresponding range for each viewing window. Show each graph. [−100, 100]
For the following exercises, use the functions f(x) = 2x2 + 1 and g(x) = 3x + 5 to evaluate or find the composite function as indicated.f( g(x))
For the following exercises, describe how the formula is a transformation of a toolkit function. Then sketch a graph of the transformation.a(x) = √−x + 4
For the following exercises, describe how the formula is a transformation of a toolkit function. Then sketch a graph of the transformation. = ( + x)²- q(x)= +1
For the following exercises, use a graphing utility to determine whether each function is one-to-one.f(x) =1/x
For the following exercises, graph y = x2 on the given viewing window. Determine the corresponding range for each viewing window. Show each graph. [−10, 10]
For the following exercises, use the functions f(x) = 2x2 + 1 and g(x) = 3x + 5 to evaluate or find the composite function as indicated.f( g(2))
For the following exercises, describe how the formula is a transformation of a toolkit function. Then sketch a graph of the transformation. p(x)=(x)²-3
For the following exercises, use each pair of functions to find f(g(0)) and g(f(0)). f(x) = x+28(x) = 4x+3
For the following exercise, find a domain on which the function f is one-to-one and non-decreasing. Write the domain in interval notation. Then find the inverse of f restricted to that domain.Given f(x) = x3 − 5 and g(x) = 3√x + 5 : a. Find f(g(x)) and g(f(x)). b. What does the answer
For the following exercises, graph y = x2 on the given viewing window. Determine the corresponding range for each viewing window. Show each graph. [−0.1, 0.1]
For the following exercises, use each pair of functions to find f(g(0)) and g(f(0)). f(x)=√x+4, g(x) = 12-x
For the following exercise, find a domain on which the function f is one-to-one and non-decreasing. Write the domain in interval notation. Then find the inverse of f restricted to that domain. f(x) = x2 + 1
For the following exercises, evaluate the expressions, given functions f, g, and h: 3f(1) − 4g(−2)
For the following exercises, describe how the formula is a transformation of a toolkit function. Then sketch a graph of the transformation.n(x) = 1 3 |x − 2|
For the following exercises, use each pair of functions to find f(g(0)) and g(f(0)). f(x) = 5x+7, g(x)=4 - 2x²
For the following exercises, find f −1 (x) for each function.f(x) = x/x + 2
For the following exercises, evaluate the expressions, given functions f, g, and h: f(x) = 3x − 2 g(x) = 5 − x2 h(x) = −2x2 + 3x − 1
For the following exercises, describe how the formula is a transformation of a toolkit function. Then sketch a graph of the transformation.m(x) =  1/2 x3
For the following exercises, find f −1 (x) for each function.f(x) = 9 + 10x
For the following exercises, evaluate the function f at the values f(−2), f(−1), f(0), f(1), and f(2). f(x) = 3x
For the following exercises, use each pair of functions to find f(g(0)) and g(f(0)). f(x) = 4x+8, g(x) = 7 - x²
For the following exercises, solve the inequality and express the solution using interval notation. 3
For the following exercises, evaluate the function f at the values f(−2), f(−1), f(0), f(1), and f(2). = f(x) = * - 2 = x+3
For the following exercises, describe how the formula is a transformation of a toolkit function. Then sketch a graph of the transformation.k(x) = −3√x − 1
For the following exercises, use the function values for f and g shown in Table 4 to evaluate the expressions.(f ∘ f)(3) -3 f(x) 11 g(x) -8 -2 -1 9 7 0 -3 بنا Table 4 0 5 1 1 3 0 2 1 -3 نرا 3 -1 -8
For the following exercises, evaluate the function f at the values f(−2), f(−1), f(0), f(1), and f(2). -f(x)=3+√x+3
For the following exercises, describe how the formula is a transformation of a toolkit function. Then sketch a graph of the transformation.h(x) = −2∣ x − 4∣ + 3
For the following exercises, solve the absolute value equation. 1px + 51=102-21
For the following exercises, use the function values for f and g shown in Table 4 to evaluate the expressions.(g ∘ g)(1) x -3 f(x) 11 g(x) -8 -2 -1 9 -3 0 7 5 1 70 Table 4 1 3 0 2 1 -3 3 -1 -8
For the following exercises, solve the inequality and express the solution using interval notation.|3x − 2| < 7
For the following exercises, use the function values for f and g shown in Table 4 to evaluate the expressions.(g ∘ f)(3) -3 f(x) 11 g(x) -8 น 4 -2 9 -3 -1 7 0 Table 4 0 5 1 1 3 نرا 0 2 1 -3 3 -1 -8
For the following exercises, describe how the formula is a transformation of a toolkit function. Then sketch a graph of the transformation.g(x) = 5(x + 3)2 − 2
For the following exercises, evaluate the function f at the values f(−2), f(−1), f(0), f(1), and f(2). f(x) = 8x2 − 7x + 3
For the following exercises, describe how the formula is a transformation of a toolkit function. Then sketch a graph of the transformation. g(x) = 4(x + 1)2 − 5
For the following exercises, solve the absolute value equation.|x + 4| = 18
For the following exercises, use the function values for f and g shown in Table 4 to evaluate the expressions. (g ∘ f)(2) -3 -2 -1 7 x f(x) 11 g(x) -8 ی 9 -3 0 Table 4 0 5 1 الا 1 3 0 2 دا 1 -3 3 -1 -8
For the following exercises, evaluate the function f at the values f(−2), f(−1), f(0), f(1), and f(2). f(x) = 8 − 3x
For the following exercises, write a formula for the function g that results when the graph of a given toolkit function is transformed as described.The graph of f(x) = x2 is horizontally stretched by a factor of 3, then shifted to the left 4 units and down 3 units.
For the following exercises, use the function values for f and g shown in Table 4 to evaluate the expressions. (f ∘ g)(2) -3 -2 9 x f(x) 11 g(x) -8 -3 -1 0 7 5 0 1 Table 4 1 3 نرا 0 2 نا نرا 1 -1 -3 -8
For the following exercises, use the function f represented in Table 14 below. Evaluate f(3). x 0 f(x) 74 1 28 2 19 1 3 نیا 53 4 5 56 3 الا نیا Table 14 6 36 7 45 00 8 14 9 47
For the following exercises, graph the absolute value function.f(x) = |2x − 4|
For the following exercises, evaluate the function f at the values f(−2), f(−1), f(0), f(1), and f(2).f(x) = 4 − 2x
For the following exercises, write a formula for the function g that results when the graph of a given toolkit function is transformed as described.The graph of f(x) = x2 is vertically compressed by a factor of 1/2, then shifted to the right 5 units and up 1 unit.
For the following exercises, use the function values for f and g shown in Table 4 to evaluate the expressions. (f ∘ g)(1) x f(x) g(x) 0 7 9 1 6 5 256 3 8 2 4 4 1 Table 3 5 0 8 629 7 1 3 8 9 4 9 3 0
For the following exercises, use the function f represented in Table 14 below. X f(x) 0 74 1 28 2 1 تها 53 4 56 Table 14 5 3 الا نیا 6 36 7 45 8 00 14 9 47
For the following exercises, graph the absolute value function.f(x) = −|x − 3|
For the following exercises, use the function values for f and g shown in Table 3 to evaluate each expression.g( g(6)) 8* 0 1 7 6 g(x) 9 25 3 4 8 4 1 Table 3 درا 0 5 6 2 5 0 8 6 2 7 00 7 8 1 9 3 4 9 3 0 درا
For the following exercises, write a formula for the function g that results when the graph of a given toolkit function is transformed as described.The graph of f(x) = 1/x is vertically stretched by a factor of 8, then shifted to the right 4 units and up 2 units.
For the following exercises, graph the absolute value function.f(x) = |x − 5|
For the following exercises, write an equation for the transformation of f(x) = |x|. x angling I ins 3-4-3-1
For the following exercises, write a formula for the function g that results when the graph of a given toolkit function is transformed as described.The graph of f(x) = 1 x2 is vertically compressed by a factor of 1/3 , then shifted to the left 2 units and down 3 units.
For the following exercises, determine if the relation represented in table form represents y as a function of x. 47 5 y 3 ا بیا 10 201404 8 14
For the following exercises, use the function values for f and g shown in Table 3 to evaluate each expression.g( g(2)) x 0 27 f(x) g(x) 7 9 165 25 3 4 4 1 Table 3 درا 0 5 8 6 2 5 0 8 629 7 1 لیا 8 600 9 4 9 3 0 درا
For the following exercises, write a formula for the function g that results when the graph of a given toolkit function is transformed as described.The graph of f(x) = √x is reflected over the x-axis and horizontally stretched by a factor of 2.
For the following exercises, write an equation for the transformation of f(x) = |x|. EN m "ay E 我
The tolerance for a ball bearing is 0.01. If the true diameter of the bearing is to be 2.0 inches and the measured value of the diameter is x inches, express the tolerance using absolute value notation.
For the following exercises, determine if the relation represented in table form represents y as a function of x. 1 x y 5 3 10 8 15 8
For the following exercises, use the function values for f and g shown in Table 3 to evaluate each expression.f(f(1)) 07 x 1 6 f(x) 7 g(x) 9 5 256 382 ا 4 4 1 Table 3 508 0 627 7 1 3 نيا 600 8 9 4 9 3 دیا 0
For the following exercises, write a formula for the function g that results when the graph of a given toolkit function is transformed as described. The graph of f(x) = ∣ x∣ is reflected over the y-axis and horizontally compressed by a factor of 1/4 .
For the following exercises, write an equation for the transformation of f(x) = |x|. x யப்பாப்பட Ho B
For the following exercises, determine if the relation represented in table form represents y as a function of x. x y 53 10 8 15 14
A machinist must produce a bearing that is within 0.01 inches of the correct diameter of 5.0 inches. Using x as the diameter of the bearing, write this statement using absolute value notation.
For the following exercises, analyze the graph and determine whether the graphed function is even, odd, or neither. EFFE -10-87 M.... 40 = $ 10 HE X
For the following exercises, use the function values for f and g shown in Table 3 to evaluate each expression.f(f(4)) x 0 f(x) 7 g(x) 9 195 25 6 3 درا 0 8 2 4 4 1 Table 3 50 0 8 627 7 1 7 3 لیا 8 600 9 4 9 3 0 دیا
For the following exercises, describe how the graph of each function is a transformation of the graph of the original function f.g(x) = −f(3x)
Students who score within 18 points of the number 82 will pass a particular test. Write this statement using absolute value notation and use the variable x for the score.
For the following exercises, determine whether the relation represents a function. (2, 5),(7, 11),(15, 8),(7, 9)}
For the following exercises, use the function values for f and g shown in Table 3 to evaluate each expression.g(f(3)) X 27 f(x) g(x) 1 7 6 9 5 0 25 6 3 4 8 4 2 1 Table 3 نا 0 5 0 8 6 2 7 600 7 1 9 3 8 4 93 3 0
For the following exercises, describe how the graph of each function is a transformation of the graph of the original function f.g(x) = 3f(−x)
For the following exercises, analyze the graph and determine whether the graphed function is even, odd, or neither. -10-3 ....in 時 5- ngu mity $ 10
The true proportion p of people who give a favorable rating to Congress is 8% with a margin of error of 1.5%. Describe this statement using an absolute value equation.
For the following exercises, determine whether the relation represents a function. {(3, 4),(4, 5),(5, 6)}
For the following exercises, describe how the graph of each function is a transformation of the graph of the original function f. - 8(x) = f(x)
For the following exercises, determine whether the relation represents a function. {(−1, −1),(−2, −2),(−3, −3)}
For the following exercises, sketch the graph of the function g if the graph of the function f is shown in Figure 4.g(x) = 3f(x) -5-4-3-2 y 5+ Figure 4 IIII. X

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