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문제 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)
문제 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)
문제 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)
문제 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)
문제 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)
문제 61
For each function, find (a) ƒ(2) and (b) ƒ(-1). See Example 7. ƒ = {(-1, 3), (4, 7), (0, 6), (2, 2)}
문제 62
For each function, find (a) ƒ(2) and (b) ƒ(-1). See Example 7. ƒ = {(2, 5), (3, 9), (-1, 11), (5, 3)}
문제 65
For each function, find (a) ƒ(2) and (b) ƒ(-1). See Example 7.
문제 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).
문제 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).
문제 71a
Determine the largest open intervals of the domain over which each function is (a) increasing See Example 8.
문제 71b
Determine the largest open intervals of the domain over which each function is (b) decreasing. See Example 8.
문제 71c
Determine the largest open intervals of the domain over which each function is (c) constant. See Example 8.
문제 75a
Determine the largest open intervals of the domain over which each function is (a) increasing See Example 8.
문제 75b
Determine the largest open intervals of the domain over which each function is (b) decreasing. See Example 8.
문제 75c
Determine the largest open intervals of the domain over which each function is (c) constant. See Example 8.
문제 81
Determine the intervals of the domain over which each function is continuous. See Example 9.
문제 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.
문제 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.
문제 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.
문제 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.
문제 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
문제 15
Graph each function. See Examples 1 and 2. ƒ(x) = 3|x|
문제 17
Graph each function. See Examples 1 and 2. ƒ(x) = ⅔ |x|
문제 19
Graph each function. See Examples 1 and 2. g(x) = 2x²
문제 21
Graph each function. See Examples 1 and 2. g(x) = ½ x²
문제 23
Graph each function. See Examples 1 and 2. ƒ(x) = -½ x²
문제 25
Graph each function. See Examples 1 and 2. ƒ(x) = -3|x|
문제 27
Graph each function. See Examples 1 and 2. h(x) = |-½ x|
문제 29
Graph each function. See Examples 1 and 2. h(x) = √4x