0. Functions

Shifting and Scaling Graphs

Suppose the graph of g is given. Write equations for the graphs that are obtained from the graph of g by shifting, scaling, or reflecting, as indicated.

f. Compress horizontally by a factor of 5

Describe how each graph is obtained from the graph of 𝔂 = ƒ(x).

a. 𝔂 = ƒ(x - 5)

Describe how each graph is obtained from the graph of 𝔂 = ƒ(x).

d. 𝔂 = ƒ(2x + 1)

Describe how each graph is obtained from the graph of 𝔂 = ƒ(x).

e. 𝔂 = ƒ( x ) - 4

3

In Exercises 55–58, graph each function, not by plotting points, but by starting with the graph of one of the standard functions presented in Figures 1.15–1.17, and applying an appropriate transformation.

y = - √(1 + x/2)

Shifting Graphs

The accompanying figure shows the graph of y = −x² shifted to two new positions. Write equations for the new graphs.

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Shifting Graphs

The accompanying figure shows the graph of y = −x² shifted to four new positions. Write an equation for each new graph.

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Shifting Graphs

Exercises 27–36 tell how many units and in what directions the graphs of the given equations are to be shifted. Give an equation for the shifted graph. Then sketch the original and shifted graphs together, labeling each graph with its equation.

y = x³ Left 1, down 1

Shifting Graphs

Exercises 27–36 tell how many units and in what directions the graphs of the given equations are to be shifted. Give an equation for the shifted graph. Then sketch the original and shifted graphs together, labeling each graph with its equation.

y = −√x Right 3

Shifting Graphs

Exercises 27–36 tell how many units and in what directions the graphs of the given equations are to be shifted. Give an equation for the shifted graph. Then sketch the original and shifted graphs together, labeling each graph with its equation.

y = (1/2)(x + 1) + 5 Down 5, right 1

Graph the functions in Exercises 37–56.

y = |x − 2|

Graph the functions in Exercises 37–56.

y = (x + 1)²/³

Graph the functions in Exercises 37–56.

y = (x + 2)³/² + 1

Graph the functions in Exercises 37–56.

y = (1/x²) − 1

Graphing

In Exercises 69–76, graph each function not by plotting points, but by starting with the graph of one of the standard functions presented in Figures 1.14–1.17 and applying an appropriate transformation.

y = (1/2x) − 1