Chapter 10, Problem 10CR

a.

To determine

To find: The equations that has a graph symmetric to $y-$ axis.

Answer to Problem 10CR

Equation $\mathrm{A}$ is not symmetric to $y-$ axis.

Explanation of Solution

Given information: Given equations is $y=-3x+9$ .

Calculation: For a graph to be symmetric to the $y-$ axis if $f\left(-x\right)=f\left(x\right)$ .

Now put $-x$ in place of $x$ in every given options

A. $f\left(x\right)=$ $-3x+9$

  $f\left(-x\right)=-3\left(-x\right)+9=3x+9\ne f\left(x\right)$

Thus they are not same.

b.

To determine

To find: The equations that has a graph symmetric to $y-$ axis.

Answer to Problem 10CR

Equation $\mathrm{B}$ is symmetric to $y-$ axis.

Explanation of Solution

Given information: Given equations is $y=3x^2+9$ .

Calculation: For a graph to be symmetric to the $y-$ axis if $f\left(-x\right)=f\left(x\right)$ .

Now put $-x$ in place of $x$ in every given options

  $y=3x^2+9$

  $f\left(-x\right)=3{\left(-x\right)}^2+9=3x^2+9=f\left(x\right)$

Thus, they are same.

c.

To determine

To find: The equations that has a graph symmetric to $y-$ axis.

Answer to Problem 10CR

Equation $\mathrm{C}$ is symmetric to $y-$ axis.

Explanation of Solution

Given information: Given equations is $y=-3x^2+9$ .

Calculation: For a graph to be symmetric to the $y-$ axis if $f\left(-x\right)=f\left(x\right)$ .

Now put $-x$ in place of $x$

  $y=-3x^2+9$

  $f\left(-x\right)=-3{\left(-x\right)}^2+9=-3x^2+9=f\left(x\right)$

Thus they are symmetric.

d.

To determine

To find: The equations that has a graph symmetric to $y-$ axis.

Answer to Problem 10CR

Equation $\mathrm{D}$ is not symmetric to $y-$ axis.

Explanation of Solution

Given information: Given equations is $y=3^x+9$ .

Calculation : For a graph to be symmetric to the $y-$ axis if $f\left(-x\right)=f\left(x\right)$ .

Now put $-x$ in place of $x$

  $y=3^x+9$

  $f\left(-x\right)=3^{-x}+9\ne f\left(x\right)$

Thus, Equation $\mathrm{D}$ is not symmetric to $y-$ axis.

e.

To determine

To find: The equations that has a graph symmetric to $y-$ axis.

Answer to Problem 10CR

Equation $\mathrm{E}$ is not symmetric to $y-$ axis.

Explanation of Solution

Given information: Given equations is $y=3^x+9$ .

Calculation: For a graph to be symmetric to the $y-$ axis if $f\left(-x\right)=f\left(x\right)$ .

Now put $-x$ in place of $x$ For a graph to be symmetric to the $y-$ axis if $f\left(-x\right)=f\left(x\right)$

  $y={\left(-3\right)}^x+9$

  $f\left(-x\right)={\left(-3\right)}^{-x}+9\ne f\left(x\right)$

Thus, Equation $\mathrm{E}$ is not symmetric to $y-$ axis.