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

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

Use graphing software to graph the functions specified in Exercises 31–36.

Select a viewing window that reveals the key features of the function.

Graph the upper branch of the hyperbola y² − 16x² = 1.

In Exercises 35 and 36, find the (a) domain and (b) range.

𝔂 = { -x - 2, -2 ≤ x ≤ - 1

{ x, -1 < x ≤ 1

{ -x + 2, 1 < x ≤ 2

[Technology Exercise]

You want to make an 80° angle by marking an arc on the perimeter of a 12-in.-diameter disk and drawing lines from the ends of the arc to the disk’s center. To the nearest tenth of an inch, how long should the arc be?

Increasing and Decreasing Functions

Graph the functions in Exercises 37–46. What symmetries, if any, do the graphs have? Specify the intervals over which the function is increasing and the intervals where it is decreasing.

y = x³/8

In Exercises 9–16, determine whether the function is even, odd, or neither.

𝔂 = x² + 1