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mathematics
precalculus 1st

Questions and Answers of Precalculus 1st

For the following exercises, use a graphing utility to estimate the local extrema of each function and to estimate the intervals on which the function is increasing and decreasing.n(x) = x4 − 8x3 +
For the following exercises, find (f ∘ g) and the domain for (f ∘ g)(x) for each pair of functions. f(x) = x + 1/x + 4 , g(x) = 1/x
For the following exercises, use the values listed in Table 6 to evaluate or solve.Find f−1 (0). x 0 f(x) 8 1 0 2 7 3 4 4 2 Table 6 5 6 6 5 7 3 8 9 9 1
For the following exercises, use the values listed in Table 6 to evaluate or solve.Solve f−1 (x) = 7. f(x) 0 8 1 0 2 7 3 4 4 2 Table 6 5 6 6 5 7 3 8 9 9 1
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)² 1 2x - 3
For the following exercises, sketch a graph of the piecewise function. Write the domain in interval notation. [x+1ifx0
For the following exercises, graph the given functions by hand. y = |x| − 2
For the following exercises, use the vertical line test to determine which graphs show relations that are function ww T y x
For the following exercises, graph the given functions by hand.y = −|x| 
For the following exercises, use the graphs of transformations of the square root function to find a formula for each of the functions. X- pinig -3+ a -$
The graph of the function f is shown in Figure 18. Based on the calculator screen shot, the point (1.333, 5.185) is which of the following?A. a relative (local) maximum of the function B.
For the following exercises, use the vertical line test to determine which graphs show relations that are function ***** I ܘܐܫ June x
For the following exercises, sketch a graph of the piecewise function. Write the domain in interval notation. if x < 0 f(x) = {1-xif x>0
For the following exercises, find the inverse function. Then, graph the function and its inverse. f(x) = 3/x − 2
For the following exercises, use the graphs of f, shown in Figure 4, and g, shown in Figure 5, to evaluate the expressions. f(g(3)) f(x) Figure 4 -X
For the following exercises, use the graphs of transformations of the square root function to find a formula for each of the functions.
For the following exercises, use the vertical line test to determine which graphs show relations that are function கெட்
For the following exercises, find (f ∘ g) and the domain for (f ∘ g)(x) for each pair of functions. f(x) = 1/x2 − 1 , g(x) = √x + 1
For the following exercises, use the graphs of the transformed toolkit functions to write a formula for each of the resulting functions.
For the following exercises, graph the given functions by hand.y = −|x| − 2
For the following exercises, use the graphs of f, shown in Figure 4, and g, shown in Figure 5, to evaluate the expressions. f( g(1)) f(x) Figure 4
For the following exercises, use the vertical line test to determine which graphs show relations that are function " IT ang x
Let f(x) = 1/x. Find a number c such that the average rate of change of the function f on the interval (1, c) is −1/4
For the following exercises, sketch a graph of the piecewise function. Write the domain in interval notation. if x < 0 _f(x) = { x + 2 if x20
For the following exercises, use the graphs of f, shown in Figure 4, and g, shown in Figure 5, to evaluate the expressions. g(f(1)) f(x) Figure 4
For the following exercises, use the vertical line test to determine which graphs show relations that are function I ge M
For the following exercises, express each function H as a composition of two functions f and g where H(x) = (f ∘ g)(x)H(x) = √ 2x − 1/3x + 4
For the following exercises, express each function H as a composition of two functions f and g where H(x) = (f ∘ g)(x) H(x) = 1 (3x² - 4)-¹
For the following exercises, graph the given functions by hand.y = −|x − 3| − 2
For the following exercises, use the graphs of the transformed toolkit functions to write a formula for each of the resulting functions.
Let f(x) = 1/x . Find the number b such that the average rate of change of f on the interval (2, b) is −1/10 .
For the following exercises, sketch a graph of the piecewise function. Write the domain in interval notation. I>x J! 1+xJ -f(x) = {x² if x 21
For the following exercises, find the inverse function. Then, graph the function and its inverse.Find the inverse function of f(x) = 1/x − 1 . Use a graphing utility to find its domain and range.
For the following exercises, graph the given functions by hand.f(x) = −|x − 1| − 2
At the start of a trip, the odometer on a car read 21,395. At the end of the trip, 13.5 hours later, the odometer read 22,125. Assume the scale on the odometer is in miles. What is the average speed
To convert from x degrees Celsius to y degrees Fahrenheit, we use the formula f(x) = 9/5 x + 32. Find the inverse function, if it exists, and explain its meaning.
For the following exercises, sketch a graph of the given function.f(x) = (x − 3)2
For the following exercises, use the graphs of f, shown in Figure 4, and g, shown in Figure 5, to evaluate the expressions. g(f(0)) f(x) Figure 4
For the following exercises, graph the given functions by hand.f(x) = −|x + 3| + 4
A driver of a car stopped at a gas station to fill up his gas tank. He looked at his watch, and the time read exactly 3:40 p.m. At this time, he started pumping gas into the tank. At exactly 3:44,
For the following exercises, sketch a graph of the piecewise function. Write the domain in interval notation. -f(x) [x|if x < 2 {1 if x 22
For the following exercises, use the graphs of the transformed toolkit functions to write a formula for each of the resulting functions.
For the following exercises, use the vertical line test to determine which graphs show relations that are function # x
For the following exercises, find the average rate of change of each function on the interval specified. p(t)= (t²-4)(t+1) t² + 3 on [-3, 1]
For the following exercises, write the domain and range of each function using interval notation. FEE j IT x
For the following exercises, write an equation for each graphed function by using transformations of the graphs of one of the toolkit functions. 5 migi +2+ mem -X
For the following exercises, use the graphs to determine the intervals on which the functions are increasing, decreasing, or constant.Find the absolute maximum of the function graphed in Figure
Given the function g(x)=x²+2x, evaluate g(x)-g(a) x-a -, xa
For the following exercises, evaluate or solve, assuming that the function f is one-to-one. If f(6) = 7, find f−1 (7).
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) 8 + x³ 8-x³
For the following exercises, use the values listed in Table 1.Find F−1 (15). x 0 F(x) 1 1 3 2 5 3 7 Table 1 4 9 10 5 11 6 13 7 15 8 17
For the following exercises, write the domain and range of each function using interval notation. TI 866 x
For the following exercises, solve each inequality and write the solution in interval notation.|3x − 5| ≥ −13
For the following exercises, find the average rate of change of each function on the interval specified. k(t) = 6f² + on [-1,3]
For the following exercises, write an equation for each graphed function by using transformations of the graphs of one of the toolkit functions. F-F Pi HA -x
For the following exercises, find (f ∘ g)(x) and (g ∘ f)(x) for each pair of functions.f(x) = 4 − x, g(x) = −4x
For the following exercises, evaluate or solve, assuming that the function f is one-to-one. If f(3) = 2, find f−1 (2).
For the following exercises, solve each inequality and write the solution in interval notation. 2x-527
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) = √2x + 6
For the following exercises, use the values listed in Table 1.Given f(x) = −2x + 11, find f−1 (x). x 0 F(x) 1 1 3 2 5 3 7 Table 1 4 9 5 11 163 13 7 15 8 17
For the following exercises, write the domain and range of each function using interval notation. LLL II (6)
For the following exercises, use a graphing utility to estimate the local extrema of each function and to estimate the intervals on which the function is increasing and decreasing. f(x) = x4 −
For the following exercises, write an equation for each graphed function by using transformations of the graphs of one of the toolkit functions. 2.8 ... 3-4-5 mpm 5+ gi p -X
For the following exercises, find (f ∘ g)(x) and (g ∘ f)(x) for each pair of functions. f(x) = 3x + 2, g(x) = 5 − 6x
For the following exercises, evaluate or solve, assuming that the function f is one-to-one.If f−1 (−4) = −8, find f(−8).
For the following exercises, solve each inequality and write the solution in interval notation. x-5|+1≤16
For the following exercises, use a graphing utility to estimate the local extrema of each function and to estimate the intervals on which the function is increasing and decreasing.h(x) = x5 + 5x4 +
For the following exercises, write an equation for each graphed function by using transformations of the graphs of one of the toolkit functions. x
For the following exercises, find functions f(x) and g(x) so the given function can be expressed as h(x) = f(g(x)). 3 h(x)=√x-1
For the following exercises, find (f ∘ g)(x) and (g ∘ f)(x) for each pair of functions. f(x) = x2 + 2x, g(x) = 5x + 1
For the following exercises, evaluate or solve, assuming that the function f is one-to-one. If f−1 (−2) = −1, find f(−1).
For the following exercises, use a graphing utility to estimate the local extrema of each function and to estimate the intervals on which the function is increasing and decreasing. g(t)=tVt+3
For the following exercises, graph the absolute value function. Plot at least five points by hand for each graph. y = |x − 1|
For the following exercises, write the domain and range of each function using interval notation. -DE II ttivate
For the following exercises, write an equation for each graphed function by using transformations of the graphs of one of the toolkit functions. died: me 10%. ipin
For the following exercises, use the values listed in Table 6 to evaluate or solve. Find f(1). x 0 f(x) 8 1 0 2 7 3 4 4 2 Table 6 5 6 6 5 7 3 8 9 9 1
For the following exercises, find (f ∘ g)(x) and (g ∘ f)(x) for each pair of functions. f(x) = √x + 2 , g(x) =1/x
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) = |x2 + 7|
For the following exercises, use a graphing utility to estimate the local extrema of each function and to estimate the intervals on which the function is increasing and decreasing. 2 k(t) = 3t-t
For the following exercises, graph the absolute value function. Plot at least five points by hand for each graph.y = |x + 1| 
For the following exercises, write an equation for each graphed function by using transformations of the graphs of one of the toolkit functions. 3-2- H y H 1
For the following exercises, use the values listed in Table 6 to evaluate or solve.Solve f(x) = 3. x 0 f(x) 8 1 0 2 7 3 4 4 2 Table 6 5 6 6 5 7 3 8 9 9 1
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 1 - 2)³
Given the function f(x) = x2 − 3x a. Evaluate ∫(5).b. Solve ∫(x) = 4.
For the following exercises, find (f ∘ g)(x) and (g ∘ f)(x) for each pair of functions. f(x) = x + 3/2 , g(x) = √1 − x
For the following exercises, write an equation for each graphed function by using transformations of the graphs of one of the toolkit functions. ke y rāmāna -x
For the following exercises, sketch a graph of the piecewise function. Write the domain in interval notation. if x < 1 (2x-1 =f(x)={1+x if x21
For the following exercises, graph the absolute value function. Plot at least five points by hand for each graph.y = |x| + 1
For the following exercises, use a graphing utility to estimate the local extrema of each function and to estimate the intervals on which the function is increasing and decreasing.m(x) = x4 + 2x3 −
Consider the relationship 3r + 2t = 18. a. Write the relationship as a function r = f(t). b. Evaluate f(−3). c. Solve f(t) = 2.
For the following exercises, write the domain and range of each function using interval notation. HE CIL IIII
For the following exercises, write the domain and range of each function using interval notation.
For the following exercises, find the inverse of the function.f(x) = 3x − 5
For the following exercises, find the domain of each function, expressing answers using interval notation. f(x) = x − 3/x2 − 4x − 12
For the following exercises, use each set of functions to find f(g(h(x))). Simplify your answers. Given f(x) = √2 - 4x and g(x)= = -3, find the following: a. (gof)(x) b. the domain of (gof)(x) in
For the following exercises, find the inverse of the function.f(x) = 4/x + 7
For the following exercises, determine the interval(s) on which the function is increasing and decreasing. 1-x^{- = (x)
For the following exercises, find the domain of each function, expressing answers using interval notation. x+1 -2x-3 Graph this piecewise function: f(x) ›={₁ x
For the following exercises, find the domain of each function using interval notation. - f(x) = = x² - 9x x-81
For the following exercises, use the graph of f shown in Figure 11. Find f(0). DI Figure 11 23 x

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