Chapter 2: Q. 10 (page 112)

In Problems 7–18, match each graph to one of the following functions:
$A . y = x^{2} + 2 B . y = - x^{2} + 2 C . y = |x| + 2 D . y = - |x| + 2 E . y = {(x - 2)}^{2} F . y = - {(x + 2)}^{2} G . y = |x - 2| H . y = - |x + 2| I . y = 2 x^{2} J . y = - 2 x^{2} K . y = 2 |x| L . y = - 2 |x|$

Short Answer

Expert verified

The given graph is matched to the function $D . y = - |x| + 2 .$

Step by step solution

Step 1. Given Information

There is the given graph we have to match each graph to its functions.

Step 2. Identifying the function of the graph

When the right side of the function $y = f (x)$ is multiplied by $- 1$ the graph of the new function $y = - f (x)$ is the reflection about the x-axis of the graph of the function $y = f (x)$ .

Thus, the function whose graph is the reflection of the graph of $y = |x|$ in the x-axis is $y = - |x| .$

Step 3. Stating the function of the graph

If a positive real number k is added to the outputs of a function $y = f (x),$ the

graph of the new function $y = f (x) + k$ is the graph of fshifted vertically up

kunits.

Since the graph of $y = - |x|$ is shifted vertically up by $2$ units.

The function of the given graph is $y = - |x| + 2$ that matched to the option D.

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In Problems 7–18, match each graph to one of the following functions:
$A . y = x^{2} + 2 B . y = - x^{2} + 2 C . y = |x| + 2 D . y = - |x| + 2 E . y = {(x - 2)}^{2} F . y = - {(x + 2)}^{2} G . y = |x - 2| H . y = - |x + 2| I . y = 2 x^{2} J . y = - 2 x^{2} K . y = 2 |x| L . y = - 2 |x|$

Short Answer

Step by step solution

Step 1. Given Information

Step 2. Identifying the function of the graph

Step 3. Stating the function of the graph

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In Problems 7–18, match each graph to one of the following functions:A.y=x2+2B.y=-x2+2C.y=x+2D.y=-x+2E.y=(x-2)2F.y=-(x+2)2G.y=x-2H.y=-x+2I.y=2x2J.y=-2x2K.y=2xL.y=-2x

Short Answer

Step by step solution

Step 1. Given Information

Step 2. Identifying the function of the graph

Step 3. Stating the function of the graph

One App. One Place for Learning.

Most popular questions from this chapter

Recommended explanations on Math Textbooks

Decision Maths

Calculus

Statistics

Discrete Mathematics

Applied Mathematics

Theoretical and Mathematical Physics

Study anywhere. Anytime. Across all devices.

In Problems 7–18, match each graph to one of the following functions:
$A . y = x^{2} + 2 B . y = - x^{2} + 2 C . y = |x| + 2 D . y = - |x| + 2 E . y = {(x - 2)}^{2} F . y = - {(x + 2)}^{2} G . y = |x - 2| H . y = - |x + 2| I . y = 2 x^{2} J . y = - 2 x^{2} K . y = 2 |x| L . y = - 2 |x|$