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mathematics
precalculus 1st

Precalculus 1st Edition Jay Abramson - Solutions

For the following exercises, given each function f, evaluate f(−1), f(0), f(2), and f(4). 51. f(x)= 5x if 3 x 3
For the following exercises, determine whether the function is odd, even, or neither.f(x) = (x − 2)2
For the following exercises, use the vertical line test to determine which graphs show relations that are function TUNING Tuku pruss IN
For the following exercises, sketch a graph of the piecewise function. Write the domain in interval notation. 3 if x
Use the tabular representation of f in Table 7 to create a table for f−1 (x). x f(x) 3 1 6 4 Table 7 9 7 13 12 14 16
For the following exercises, use graphs of f(x), shown in Figure 6, g(x), shown in Figure 7, and h(x), shown in Figure 8, to evaluate the expressions. f( g(4)) f(x) Figure 6 Figure 7 hond h(x) f(x) Figure 8
For the following exercises, write the domain for the piecewise function in interval notation. x+1 if x < 2 ・f(x) f(x) = {-2x-3 if x>-2
For the following exercises, graph the given functions by hand.f(x) = 1/2|x + 4| − 3
For the following exercises, determine whether the function is odd, even, or neither. h(x)=2x-x³
Given the following graph a. Evaluate f(−1). b. Solve for f(x) = 3. III. IIIII
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) = f(x − 1) Sinau 5+ -5- -4-3-2 3-2-1. Figure 4
For the following exercises, use graphs of f(x), shown in Figure 6, g(x), shown in Figure 7, and h(x), shown in Figure 8, to evaluate the expressions.f( g(1)) [(x) f(x) Figure 6 f(x) Figure 7 (x)! h(x) f(x) Figure 8
Use a graphing utility to graph f(x) = 10|x − 2| on the viewing window [0, 4]. Identify the corresponding range. Show the graph.
For the following exercises, write the domain for the piecewise function in interval notation. x² -2 if x < 1 1-x²+2 if x>1 f(x) = { *
For the following exercises, use graphs of f(x), shown in Figure 6, g(x), shown in Figure 7, and h(x), shown in Figure 8, to evaluate the expressions. f(h(2)) Figure 6 f(x) Figure 7 (x) f(x) Figure 8
Given the following graph a. Evaluate f(0). b. Solve for f(x) = −3. 표 J #
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(x)
For the following exercises, write the domain for the piecewise function in interval notation. -f(x)= 2x-3 1-3.x² if x < 0 if x ≥ 2
Use a graphing utility to graph f(x) = −100|x| + 100 on the viewing window [−5, 5]. Identify the corresponding range. Show the graph.
Given the following graph a. Evaluate f(4). b. Solve for f(x) = 1. [T Jeff p -$- ****
For the following exercises, write the equation for the standard function represented by each of the graphs below. E -X
For the following exercises, use graphs of f(x), shown in Figure 6, g(x), shown in Figure 7, and h(x), shown in Figure 8, to evaluate the expressions. h(f(2)) f(x) Figure 6 f(x) Figure 7 g(x) f(x) Figure 8
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(−x)
For the following exercises, graph each function using a graphing utility. Specify the viewing window. f(x) = −0.1|0.1(0.2 − x)| + 0.3
Graph y = 1/x2 on the viewing window [−0.5, −0.1] and [0.1, 0.5]. Determine the corresponding range for the viewing window. Show the graphs.
For the following exercises, use graphs of f(x), shown in Figure 6, g(x), shown in Figure 7, and h(x), shown in Figure 8, to evaluate the expressions. f( g(h(4))) j(x) f(x) Figure 6 f(x) Figure 7 g(x) h(x) f(x) Figure 8
For the following exercises, determine if the given graph is a one-to-one function. BA qu У B #
For the following exercises, write the equation for the standard function represented by each of the graphs below. y mann -x
For the following exercises, determine if the given graph is a one-to-one function. aquaquagado HI
For the following exercises, describe how the graph of each function is a transformation of the graph of the original function f.g(x) = 4f(x)
For the following exercises, determine if the given graph is a one-to-one function. x Gender pingg
For the following exercises, use graphs of f(x), shown in Figure 6, g(x), shown in Figure 7, and h(x), shown in Figure 8, to evaluate the expressions. f( g(f(−2))) [(x) f(x) Figure 6 Figure 7 (x) h(x) f(x) Figure 8
For the following exercises, graph each function using a graphing utility. Specify the viewing window. f(x) = 4 × 109 ∣ x − (5 × 109)∣ + 2 × 109
Graph y = 1/x on the viewing window [−0.5, −0.1] and [0.1, 0.5]. Determine the corresponding range for the viewing window. Show the graphs.
For the following exercises, describe how the graph of each function is a transformation of the graph of the original function f.g(x) = 6f(x)
For the following exercises, determine whether each function below is even, odd, or neither.f(x) = 3x4
For the following exercises, solve the inequality. |−2x − 2/3 (x + 1)| + 3 > −1
For the following exercises, use the function values for f and g shown in Table 3 to evaluate each expression. f( g(8)) x 0 f(x) 7 g(x) 9 12 6 5 5 6 3 8 2 4 4 1 Table 3 50 8 6 2 7 7 1 3 8 9 9 3 4 0 درا
Suppose the range of a function f is [−5, 8]. What is the range of |f(x)|?
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(5x)
For the following exercises, determine if the given graph is a one-to-one function. # ஈவிர டர் meizm Pow
For the following exercises, determine whether each function below is even, odd, or neither.g(x) = √x
For the following exercises, solve the inequality. If possible, find all values of a such that there are no x-intercepts for f(x) = 2|x + 1| + a.
For the following exercises, use the function values for f and g shown in Table 3 to evaluate each expression.f( g(5)) x 0 f(x) g(x) 9 91 7 6 5 25 5 6 3 4 4 1 Table 3 درا 0 8 2 5 0 8 627 7 1 لیا 8 9 600 9 4 درا 0
Create a function in which the range is all nonnegative real numbers.
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(2x)
For the following exercises, determine whether each function below is even, odd, or neither.h(x) = 1/x + 3x
For the following exercises, solve the inequality.If possible, find all values of a such that there are no y-intercepts for f(x) = 2|x + 1| + a.
Create a function in which the domain is x > 2.
For the following exercises, determine if the given graph is a one-to-one function. 표 #=
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, analyze the graph and determine whether the graphed function is even, odd, or neither. 25- 582 45- mon 00 25-20-510/5 5 10 15 20 25 ang 5+ 200 H x
For the following exercises, use the function values for f and g shown in Table 3 to evaluate each expression.g(f(5)) 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 7 8 1 9 3 4 9 3 0
For the following exercises, sketch a graph of the piecewise function. Write the domain in interval notation. [x+1 if x < -2 -f(x)={-2x-3if x2-2
For the following exercises, write an equation for each graphed function by using transformations of the graphs of one of the toolkit functions. y
Cities A and B are on the same east-west line. Assume that city A is located at the origin. If the distance from city A to city B is at least 100 miles and x represents the distance from city B to city A, express this using absolute value notation.
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) = (5x − 1)3
For the following exercises, find (f ∘ g) and the domain for (f ∘ g)(x) for each pair of functions.f(x) = 1/x + 3 , g(x) = 1/x − 9
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)=V 2x - 1 3x + 4
For the following exercises, find (f ∘ g) and the domain for (f ∘ g)(x) for each pair of functions. f(x) = 1/x , g(x) = √x
For the following exercises, use the graphs of f, shown in Figure 4, and g, shown in Figure 5, to evaluate the expressions.f(f(5)) f(x) Figure 4
For the following exercises, find the inverse function. Then, graph the function and its inverse. f(x) = x3 − 1
The circumference C of a circle is a function of its radius given by C(r) = 2πr. Express the radius of a circle as a function of its circumference. Call this function r(C). Find r(36π) and interpret its meaning.
For the following exercises, sketch a graph of the given function.f(x) = (x + 4)3
For the following exercises, given each function f, evaluate f(−3), f(−2), f(−1), and f(0). (x+1 if x < -2 1-2x-3 if x2-2 f(x) = { 32
For the following exercises, use the graphs of the transformed toolkit functions to write a formula for each of the resulting functions. 5-1 செய்லாய y Si III filly Imag x
For the following exercises, graph the given functions by hand.f(x) = 2|x + 3| + 1
Near the surface of the moon, the distance that an object falls is a function of time. It is given by d(t) = 2.6667t2, where t is in seconds and d(t) is in feet. If an object is dropped from a certain height, find the average velocity of the object from t = 1 to t = 2.
For the following exercises, use the vertical line test to determine which graphs show relations that are function X
For the following exercises, use the graphs of f, shown in Figure 4, and g, shown in Figure 5, to evaluate the expressions.f(f(4)) f(x) M Figure 4
A car travels at a constant speed of 50 miles per hour. The distance the car travels in miles is a function of time, t, in hours given by d(t) = 50t. Find the inverse function by expressing the time of travel in terms of the distance traveled. Call this function t(d). Find t(180) and interpret its
For the following exercises, sketch a graph of the given function.f(x) = √x + 5
For the following exercises, graph the given functions by hand.f(x) = 3|x − 2| + 3
He graph in Figure 19 illustrates the decay of a radioactive substance over t days. Amount (milligrams) A 164 14+ 12+ 10- 10 20 Time (days) Figure 19 Use the graph to estimate the average decay rate from t = 5 to t = 15. 15
For the following exercises, given each function f, evaluate f(−3), f(−2), f(−1), and f(0). f(x) = { if x≤-3 0 if x>-3
For the following exercises, use the vertical line test to determine which graphs show relations that are function www w mem НА
For the following exercises, given each function f, evaluate f(−3), f(−2), f(−1), and f(0). ·f(x) = -2x²+3 5x-7 if x≤-1 if x>-1
For the following exercises, use the graphs of f, shown in Figure 4, and g, shown in Figure 5, to evaluate the expressions.g( g(2)) f(x) Figure 4
For the following exercises, determine whether the function is odd, even, or neither. f(x) = 3x4
For the following exercises, sketch a graph of the given function.f(x) = −x3
For the following exercises, graph the given functions by hand.f(x) = |2x − 4| − 3
For the following exercises, use the graphs of f, shown in Figure 4, and g, shown in Figure 5, to evaluate the expressions.g( g(0)) f(x) Figure 4 ·x
For the following exercises, given each function f, evaluate f(−1), f(0), f(2), and f(4). - f(x)= (7x+3 [7x+6 if x < 0 if x ≥ 0
For the following exercises, determine whether the function is odd, even, or neither.g(x) = √x
For the following exercises, sketch a graph of the given function.f(x) = 3√−x
For the following exercises, use the vertical line test to determine which graphs show relations that are function [I F
For the following exercises, graph the given functions by hand.f(x) = |3x + 9| + 2
For the following exercises, use graphs of f(x), shown in Figure 6, g(x), shown in Figure 7, and h(x), shown in Figure 8, to evaluate the expressions. g(f(1)) 2 f(x) Figure 6 f(x) Figure 7 (x) h(x) 34 Figure 8
For the following exercises, determine whether the function is odd, even, or neither.h(x) = 1/x + 3x
For the following exercises, sketch a graph of the given function.f(x) = 5√−x − 4
For the following exercises, graph the given functions by hand.f(x) = −|x − 1| − 3
For the following exercises, given each function f, evaluate f(−1), f(0), f(2), and f(4). if x < 2 (x²-2 -f(x)=4+x-5| if x ≥ 2
For the following exercises, use the vertical line test to determine which graphs show relations that are function i- O MỘ #
For the following exercises, use graphs of f(x), shown in Figure 6, g(x), shown in Figure 7, and h(x), shown in Figure 8, to evaluate the expressions. g(f(2)) (x) Figure 6 f(x) Figure 7 g(x) h(x) f(x) Figure 8
For the following exercises, sketch a graph of the given function.f(x) = 4[∣x − 2∣ − 6]
For the following exercises, use the vertical line test to determine which graphs show relations that are function x m II
For the following exercises, graph the given functions by hand.f(x) = −|x + 4| −3
For the following exercises, determine whether the function is odd, even, or neither.g(x) = 2x4
For the following exercises, sketch a graph of the given function.f(x) = −(x + 2)2 − 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.n(x) = x4 − 8x3 + 18x2 − 6x + 2

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