Math  /  Algebra

QuestionThe graph of a function gg is shown below. Find g(2)g(-2) and find one value of xx for which g(x)=5g(x)=-5. (a) g(2)=g(-2)= \square (b) One value of xx for which g(x)=5:0g(x)=-5: 0

Studdy Solution

STEP 1

What is this asking? This problem is asking us to find the *y*-value of the function gg when x=2x = -2 and to find an *x*-value that makes g(x)=5g(x) = -5.
Basically, we're playing "find the coordinates" on a graph! Watch out! Don't mix up the *x* and *y* values!
Remember, g(2)g(-2) means "find the *y*-value when x=2x = -2."

STEP 2

1. Find *g*(-2)
2. Find *x* when *g*(x) = -5

STEP 3

Alright, let's **locate** x=2x = -2 on the *x*-axis.
Imagine walking along the *x*-axis until you get to 2-2.

STEP 4

Now, **draw** a vertical line straight up (or down) from x=2x = -2 until it **intersects** the graph of the function gg.

STEP 5

**Check** the *y*-coordinate of this intersection point.
That *y*-value is g(2)g(-2).
Looking at the graph, the intersection point is (2,1)(-2, 1).

STEP 6

So, g(2)=1g(-2) = 1.
We found it!

STEP 7

This time, we're given the *y*-value, which is g(x)=5g(x) = -5, and we need to find the *x*-value.

STEP 8

**Locate** 5-5 on the *y*-axis.

STEP 9

**Draw** a horizontal line straight across from y=5y = -5 until it **intersects** the graph of gg.

STEP 10

**Check** the *x*-coordinate of this intersection point.
That *x*-value is what we're looking for!
The graph intersects the horizontal line at two points, approximately (3.2,5)(-3.2, -5) and (3.2,5)(3.2, -5).

STEP 11

The problem asks for *one* value of xx, so we can choose either one.
Let's pick x3.2x \approx 3.2.

STEP 12

g(2)=1g(-2) = 1 One value of xx for which g(x)=5g(x) = -5 is approximately 3.23.2.

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