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mathematics
precalculus 1st

Questions and Answers of Precalculus 1st

Are one-to-one functions either always increasing or always decreasing? Why or why not?
For the following exercises, determine whether the relation represents a function.{(a, b), (c, d), (a, c)}
For the following exercises, evaluate the function f(x) = −3x2 + 2x at the given input.Find the average rate of change of the function f(b)-f(a) f(x)=3-2x²+x by finding b-a
Show that the function f(x) = a − x is its own inverse for all real numbers a.
Given f(x) = −3x2 + x and g(x) = 5, find f + g, f − g, fg, and f/g . Determine the domain for each function in interval notation.
For the following exercises, determine whether the relation represents a function.{(a, b),(b, c),(c, c)}
For the following exercises, use each pair of functions to find f(g(x)) and g(f(x)). Simplify your answers. 1 - f(x)= 8(x) = 9-x 9+2=
Given f(x) = 1/x − 4 and g(x) = 1/6 − x , find f + g, f − g, fg, and f/g . Determine the domain for each function in interval notation.
Given f(x) = √ x and g(x) = |x − 3|, find g/f . Determine the domain for each function in interval notation
For the following exercises, find the average rate of change of each function on the interval specified for real numbers b or h.a(t) = 1/t + 4 on [9, 9 + h]
For the following exercises, determine whether the relation represents y as a function of x y= 3x + 5 7x-1
For the following exercises, graph the functions by translating, stretching, and/or compressing a toolkit function. f(x) = 1/x + 2 − 1
For the following exercises, consider the graph of f shown in Figure 15. Estimate the average rate of change from x = 2 to x = 5. 7 5 4 3 Figure 15 x
For the following exercises, find a domain on which each 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
For the following exercises, find the domain of each function using interval notation. f(x) = x-3 x² + 5x-22
For the following exercises, determine whether the functions are even, odd, or neither.f(x) = −5/x3 + 9x5
For the following exercises, use Figure 2 to approximate the values.If f(x) = 1, then solve for x. -4-3- 14. " y Figure 2 I 45
For the following exercises, use each pair of functions to find f(g(x)) and g(f(x)). Simplify your answers. 1 -f(x)= ,g(x)= x-4 2-x +4
For the following exercises, determine whether the functions are even, odd, or neither. f(x) = 1/x
For the following exercises, solve the equations below and express the answer using set notation.5|x − 4| − 7 = 2
For the following exercises, use the graph of each function to estimate the intervals on which the function is increasing or decreasing. HE gram
For the following exercises, find the domain of each function using interval notation. f(x) = 2x³ - 250 x² - 2x - 15
For the following exercises, describe how the graph of the function is a transformation of the graph of the original function f. y = f(x) − 7
For the following exercises, find the domain of each function using interval notation. f(x) = 1 9-x-x
For the following exercises, use the graph of each function to estimate the intervals on which the function is increasing or decreasing. x Dumpur Der I
For the following exercises, use the function h(t) = −16t2 + 80t to find the values. h(a) - h(1) a-1
For the following exercises, use function composition to verify that f(x) and g(x) are inverse functions. f(x) = 3√x − 1 and g (x) = x3 + 1
For the following exercises, determine whether the functions are even, odd, or neither. Graph the absolute value function f(x) = −2|x − 1| + 3.
For the following exercises, solve the equations below and express the answer using set notation.0 = −|x − 3| + 2
For the following exercises, use function composition to verify that f(x) and g(x) are inverse functions.f(x) = −3x + 5 and g (x) = x − 5/−3
For the following exercises, use each set of functions to find f(g(h(x))). Simplify your answers. f(x) = x4 + 6, g(x) = x − 6, and h(x) = √x
For the following exercises, describe how the graph of the function is a transformation of the graph of the original function f. y = f(x − 2) +3
For the following exercises, solve the equations below and express the answer using set notation.2|x − 3| + 1 = 2
For the following exercises, determine whether the relation represents y as a function of x. x2 + y 2 = 9
For the following exercises, determine whether the functions are even, odd, or neither. Solve |2x − 3 | = 17.
For the following exercises, determine whether the relation represents y as a function of x.2xy = 1
For the following exercises, describe how the graph of the function is a transformation of the graph of the original function f. y = f(x + 4) − 1
For the following exercises, use the function h(t) = −16t2 + 80t to find the values. h(2) − h(1)/2 − 1
For the following exercises, use a graphing utility to determine whether each function is one-to-one. f(x) = √x
For the following exercises, use each set of functions to find f(g(h(x))). Simplify your answers. f(x) = x2 + 1, g(x) = 1/x , and h(x) = x + 3
For the following exercises, determine whether the functions are even, odd, or neither. Express the solution in interval notation. Solve-x-3217
For the following exercises, use the graphs to determine the intervals on which the functions are increasing, decreasing, or constant.Find the local minimum of the function graphed in Exercise
For the following exercises, solve each inequality and write the solution in interval notation.2|v − 7| − 4 ≥ 42
For the following exercises, use the graph of the one-to-one function shown in Figure 12. Find f(6) and f−1 (2).
For the following exercises, find the average rate of change of each function on the interval specified. q(x) = x3 on [−4, 2]
For the following exercises, find functions f(x) and g(x) so the given function can be expressed as h(x) = f(g(x)). h(x)= 3 1 2x3
For the following exercises, sketch a graph of the function as a transformation of the graph of one of the toolkit functions.m(t) = 3 + √t + 2
For the following exercises, use the values listed in Table 1. Solve the equation F(x) = 5. X 0 F(x) 1 1 3 2 5 3 7 نیا Table 1 4 9 5 11 6 13 7 15 8 17
For the following exercises, use the graph of f shown in Figure 11.Solve f(x) = 0. Figure 11 Sans
For the following exercises, use the graph of the piecewise function shown in Figure 2. Find f(2). N Figure 2
For the following exercises, solve each inequality and write the solution in interval notation.|3x − 4| ≤ 8
Table 4 gives the population of a town (in thousands) from 2000 to 2008. What was the average rate of change of population (a) between 2002 and 2004, and (b) between 2002 and 2006?
For the following exercises, find functions f(x) and g(x) so the given function can be expressed as h(x) = f(g(x)).h(x) = (x − 5)3
For the following exercises, write the domain and range of each function using interval notation. JAN fond ··
For the following exercises, find the x- and y-intercepts of the graphs of each function.f(x) = −3|x − 2| − 1
For the following exercises, use the graph of f shown in Figure 11.Find f−1 (0). # Figure 11
For the following exercises, use the graphs to determine the intervals on which the functions are increasing, decreasing, or constant. x- பப்பாயே Any 1Q ரபாட்பா OF
For the following exercises, evaluate the function f at the indicated values f(−3), f(2), f(−a), −f(a), f(a + h). f(x) = 2x − 5
For the following exercises, use the vertical line test to determine if the relation whose graph is provided is a function. x ping
For the following exercises, describe how the graph of the function is a transformation of the graph of the original function f. y = f(x + 43)
For the following exercises, determine whether the relation represents y as a function of x 3x2+ y = 14
For the following exercises, find the domain of each function using interval notation. f(x) = √ x 2+ 4
For the following exercises, find f−1 (x) for each function.f (x) = x/x + 2
Given f(x) = 2x2 + 1 and g(x) = 3x − 5, find the following: A. f( g(2)) B. f( g(x)) C. g( f(x)) D. ( g ∘ g)(x) E. ( f ∘ f)(−2)
For the following exercises, use the functions f(x) = 3 − 2x2 + x and g(x) = √x to find the composite functions.(g ∘ f)(1)
For the following exercises, solve the equations below and express the answer using set notation.|5x − 2| = 11
For the following exercises, find the average rate of change of each function on the interval specified for real numbers b or h.b(x) = 1/ x + 3 on [1, 1 + h]
For the following exercises, describe how the graph of the function is a transformation of the graph of the original function f. y = f(x + 3)
For the following exercises, graph the functions.f(x) = ∣x + 1∣
For the following exercises, determine whether the relation represents y as a function of x 2x + y2 = 6
For the following exercises, find the domain of each function using interval notation. f(x) = 3√ 1 − 2x
For the following exercises, find f−1 (x) for each function.f(x) = 2x + 3/5x + 4
For the following exercises, use each pair of functions to find f(g(x)) and g(f(x)). Simplify your answers. f(x)=x²+1, g(x)=√x+2
For the following exercises, use the functions f(x) = 3 − 2x2 + x and g(x) = √x to find the composite functions.Express H(x) = 3√5x2 − 3x as a composition of two functions, f and g, where (f
For the following exercises, solve the equations below and express the answer using set notation.|4x − 2| = 11
For the following exercises, find the average rate of change of each function on the interval specified for real numbers b or h.j(x) = 3x3 on [1, 1 + h]
For the following exercises, describe how the graph of the function is a transformation of the graph of the original function f. y = f(x − 4)
For the following exercises, graph the functions. f(x) = x2 − 2
For the following exercises, determine whether the relation represents y as a function of x y = −2x2 + 40x
For the following exercises, find the domain of each function using interval notation. f(x)=√x-1
For the following exercises, use each pair of functions to find f(g(x)) and g(f(x)). Simplify your answers. -f(x)=√x+2, g(x)=x² + 3
For the following exercises, use Figure 2 to approximate the values.f(2) 2-5-1---E y Figure 2 ingi 2 3 4 5
For the following exercises, use each pair of functions to find f(g(x)) and g(f(x)). Simplify your answers. -f(x)= x, g(x) = 5x + 1
For the following exercises, find a domain on which each function f is one-to-one and non-decreasing. Write the domain in interval notation. Then find the inverse of f restricted to that
For the following exercises, find the domain of each function using interval notation. f(x) = 9 x-6
For the following exercises, graph the functions by translating, stretching, and/or compressing a toolkit function. f(x) = √x + 6 − 1
For the following exercises, solve the equations below and express the answer using set notation.2|4 − x| = 7
For the following exercises, use Figure 2 to approximate the values.f(−2) ته ma Figure 2 8:0 3.4 -x
For the following exercises, find the average rate of change of each function on the interval specified for real numbers b or h.r(t) = 4t3 on [2, 2 + h]
For the following exercises, find the average rate of change of each function on the interval specified for real numbers b or h. f(x+h)-f(x) h given f(x)=2x²-3x on [x, x + h]
For the following exercises, determine whether the relation represents y as a function of x X= Зу +5 7y-1
For the following exercises, describe how the graph of the function is a transformation of the graph of the original function f. y = f(x) + 5
For the following exercises, find the domain of each function using interval notation. f(x) = 3x + 1 4x + 2 +2
For the following exercises, determine whether the relation represents y as a function of x y = 1/x
For the following exercises, find a domain on which each 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)
For the following exercises, solve the equations below and express the answer using set notation.3|5 − x| = 5
For the following exercises, use each pair of functions to find f(g(x)) and g(f(x)). Simplify your answers. -f(x)=√x, g(x)= x+1 x²³
For the following exercises, describe how the graph of the function is a transformation of the graph of the original function f. y = f(x) + 8
For the following exercises, find a domain on which each 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)
For the following exercises, determine whether the functions are even, odd, or neither. f(x) = −5/x2 + 9x6

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