Chapter 2.4, Problem 25AYU

If $f(x)=\{\begin{array}{cc}-x^2& ifx<0\\ 4& ifx=0\\ 3x-2& ifx>0\end{array}$ find :

$f(-3)$

(b) $f(0)$

(c) $f(3)$

To determine

The value of $f(-3)$ where the function is $f(x)=\{\begin{array}{l}-x^2\text{if}x<0\\ 4\text{if}x=0\\ 3x-2\text{if}x>0\end{array}$

Answer to Problem 25AYU

Solution:

The value of $f(-3)$ is $-9$.

Explanation of Solution

Given Information:

The function, $f(x)=\{\begin{array}{l}-x^2\text{if}x<0\\ 4\text{if}x=0\\ 3x-2\text{if}x>0\end{array}$

Explanation:

In $f(-3)$, $x=-3<0$.

Observe that for $x<0$, $f\left(x\right)=-x^2$.

Then, to find the value of $f(-3)$, plug in $x=-3$ in $f\left(x\right)=-x^2$.

$\Rightarrow f(-3)=-{\left(-3\right)}^2$

$=-\left(9\right)$

$=-9$

Hence, the value of $f(-3)$ is $-9$.

To determine

The value of $f(0)$ where the function is $f(x)=\{\begin{array}{l}-x^2\text{if}x<0\\ 4\text{if}x=0\\ 3x-2\text{if}x>0\end{array}$.

Answer to Problem 25AYU

Solution:

The value of $f(0)$ is 4.

Explanation of Solution

Given Information:

The function, $f(x)=\{\begin{array}{l}-x^2\text{if}x<0\\ 4\text{if}x=0\\ 3x-2\text{if}x>0\end{array}$

Explanation:

Observe that at $x=0$, $f\left(x\right)=4$.

Therefore, $f(0)=4$

Hence, the value of $f(0)$ is 4.

To determine

The value of $f(3)$ where the function is $f(x)=\{\begin{array}{l}-x^2\text{if}x<0\\ 4\text{if}x=0\\ 3x-2\text{if}x>0\end{array}$.

Answer to Problem 25AYU

Solution:

The value of $f\left(3\right)$ is 7.

Explanation of Solution

Given Information:

The function, $f(x)=\{\begin{array}{l}-x^2\text{if}x<0\\ 4\text{if}x=0\\ 3x-2\text{if}x>0\end{array}$

Explanation:

In $f\left(3\right)$, $x=3>0$.

Observe that for $x>0$, $f\left(x\right)=3x-2$

Then, to find the value of $f(3)$, plug in $x=3$ in $f\left(x\right)=3x-2$.

$\Rightarrow f(3)=3\left(3\right)-2$

$=9-2$

$=7$

Hence, the value of $f\left(3\right)$ is 7.