Q. 32 - Precalculus Enhanced with Graphing Utilities

Question

In parts (a) – (f), use the following figure. 

(a) Solve $g\left(x\right)= 20$.                         (b) Solve $g\left(x\right)=60$.

(c) Solve $g\left(x\right)= 0$.                           (d) Solve $g\left(x\right)>20$.

(e) Solve $g\left(x\right)\le 60.$                         ( f ) Solve $0<g\left(x\right)<60$.

Step-by-Step Solution

Answer

Part (a)  $x=5$

Part (b) $x=-15$

Part (c)  $x=15$

Part (d)  $x<5$

Part (e)  $x\ge -15$

Part (f) $-15<x<15$

Part (a) Step 1. Given information.

The graph is given.

Answer the question using the graph.

Part (a) Step 2. Explanation.

To solve $g\left(x\right)=20$

We know that, $g\left(x\right)=y$ so, $y=20$

From graph we can find corresponding value of x. 

So, we have point $\left(5,20\right)$ on the given graph. So, $x=5$

So, $x=5$ when $g\left(x\right)=20$

Part (b) Step 1. Explanation.

To solve $g\left(x\right)=60$

We know that, $g\left(x\right)=y$ so, $y=60$

From graph we can find corresponding value of x. 

So, we have point $\left(-15,60\right)$ on the given graph. So, $x=-15$

So, $x=-15$ when $g\left(x\right)=60$

Part (c) Step 1. Explanation.

To solve $g\left(x\right)=0$

We know that, $g\left(x\right)=y$  so, $y=0$.

From graph we can find corresponding value of x. 

So, we have point $\left(15,0\right)$ on the given graph. So, $x=15$.

So, $x=15$ when $g\left(x\right)=0$

Part (d) Step 1. Explanation.

To solve $g\left(x\right)>20$

We know that, $g\left(x\right)=y$ so, $y>20$

From graph we can find corresponding value of x. 

So, we have point $\left(5,20\right)$ on the given graph. So, $x=5$

The value of y is decreasing with respect to x. 

If $y>20\Rightarrow x<5$

Part (e) Step 1. Explanation.

To solve $g\left(x\right)\le 60$.

We know that, $g\left(x\right)=y$  so, $y=60$.

From graph we can find corresponding value of x. 

So, we have point $\left(-15,60\right)$ on the given graph. So, $x=-15$

The value of y is decreasing with respect to x. 

So, $y\le 60$ then $x\ge -15$

Part (f) Step 1. Explanation.

To solve $0<g\left(x\right)<60$.

We know that, $g\left(x\right)=y$ so, $0<y<60$.

 

From graph we can find corresponding value of x. 

So, we have points $\left(15,0\right), \left(-15,60\right)$ on the given graph.

The value of y is decreasing with respect to x. 

So, $0<y<60\Rightarrow -15<x<15$