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Problem 45
Let f(x) = -3x + 4 and g(x) = -x² + 4x + 1. Find each of the following. Simplify if necessary. See Example 6. ƒ(0)
Problem 47
Let f(x) = -3x + 4 and g(x) = -x² + 4x + 1. Find each of the following. Simplify if necessary. See Example 6. g(-2)
Problem 49
Let f(x) = -3x + 4 and g(x) = -x² + 4x + 1. Find each of the following. Simplify if necessary. See Example 6. ƒ(⅓)
Problem 53
Let f(x) = -3x + 4 and g(x) = -x² + 4x + 1. Find each of the following. Simplify if necessary. See Example 6. ƒ(p)
Problem 57
Let f(x) = -3x + 4 and g(x) = -x² + 4x + 1. Find each of the following. Simplify if necessary. See Example 6. ƒ(x + 2)
Problem 61
For each function, find (a) ƒ(2) and (b) ƒ(-1). See Example 7. ƒ = {(-1, 3), (4, 7), (0, 6), (2, 2)}
Problem 62
For each function, find (a) ƒ(2) and (b) ƒ(-1). See Example 7. ƒ = {(2, 5), (3, 9), (-1, 11), (5, 3)}
Problem 65
For each function, find (a) ƒ(2) and (b) ƒ(-1). See Example 7.
Problem 67
Use the graph of y = ƒ(x) to find each function value: (a) ƒ(-2) (b) ƒ(0) (c) ƒ(1) and (d) ƒ(4). See Example 7(d).
Problem 69
Use the graph of y = ƒ(x) to find each function value: (a) ƒ(-2) (b) ƒ(0) (c) ƒ(1) and (d) ƒ(4). See Example 7(d).
Problem 71a
Determine the largest open intervals of the domain over which each function is (a) increasing See Example 8.
Problem 71b
Determine the largest open intervals of the domain over which each function is (b) decreasing. See Example 8.
Problem 71c
Determine the largest open intervals of the domain over which each function is (c) constant. See Example 8.
Problem 75a
Determine the largest open intervals of the domain over which each function is (a) increasing See Example 8.
Problem 75b
Determine the largest open intervals of the domain over which each function is (b) decreasing. See Example 8.
Problem 75c
Determine the largest open intervals of the domain over which each function is (c) constant. See Example 8.
Problem 81
Determine the intervals of the domain over which each function is continuous. See Example 9.
Problem 1
Fill in the blank(s) to correctly complete each sentence.
To graph the function ƒ(x) = x² - 3, shift the graph of y = x² down ___ units.
Problem 3
Fill in the blank(s) to correctly complete each sentence.
The graph of ƒ(x) = (x + 4)² is obtained by shifting the graph of y = x² to the ___ 4 units.
Problem 5
Fill in the blank(s) to correctly complete each sentence.
The graph of ƒ(x) = -√x is a reflection of the graph of y = √x across the ___-axis.
Problem 6
Fill in the blank(s) to correctly complete each sentence.
The graph of ƒ(x) = √-x is a reflection of the graph of y = √x across the ___-axis.
Problem 11
Work each matching problem.
Match each equation in Column I with a description of its graph from Column II as it relates to the graph of y = x².
I II
a. y = (x - 7)² A. a translation to the left 7 units
b. y = x² - 7 B. a translation to the right 7 units
c. y = 7x² C. a translation up 7 units
d. y = (x + 7)² D. a translation down 7 units
e. y = x² + 7 E. a vertical stretching by a factor of 7
Problem 15
Graph each function. See Examples 1 and 2. ƒ(x) = 3|x|
Problem 17
Graph each function. See Examples 1 and 2. ƒ(x) = ⅔ |x|
Problem 19
Graph each function. See Examples 1 and 2. g(x) = 2x²
Problem 21
Graph each function. See Examples 1 and 2. g(x) = ½ x²
Problem 23
Graph each function. See Examples 1 and 2. ƒ(x) = -½ x²
Problem 25
Graph each function. See Examples 1 and 2. ƒ(x) = -3|x|
Problem 27
Graph each function. See Examples 1 and 2. h(x) = |-½ x|
Problem 29
Graph each function. See Examples 1 and 2. h(x) = √4x