Question
\( f( \) If \( f(x) \) is defined as follows, find \( (a) f(-3),(b) f(0) \), and \( (c) f(1) \) \( f(x)=\left\{\begin{array}{ll}x^{2} & \text { if } x<0 \\ -3 & \text { if } x=0 \\ 3 x+2 & \text { if } x>0\end{array}\right. \) \( \begin{array}{l}\text { (a) } f(-3)=9 \text { (Simplify your answer.) } \\ \text { (b) } f(0)=\square \text { (Simplify your answer.) }\end{array} \)
Ask by Fowler Hills. in the United States
Feb 04,2025
Real Tutor Solution
Tutor-Verified Answer
Answer
\( f(-3) = 9 \), \( f(0) = -3 \), and \( f(1) = 5 \).
Solution
Sure, let's evaluate the function \( f(x) \) for the given values step by step.
The function \( f(x) \) is defined as:
\[
f(x) = \begin{cases}
x^{2} & \text{if } x < 0 \\
-3 & \text{if } x = 0 \\
3x + 2 & \text{if } x > 0
\end{cases}
\]
### (a) \( f(-3) \)
Since \(-3 < 0\), we use the first case of the function:
\[
f(-3) = (-3)^{2} = 9
\]
### (b) \( f(0) \)
Here, \( x = 0 \), so we use the second case of the function:
\[
f(0) = -3
\]
### (c) \( f(1) \)
Since \(1 > 0\), we use the third case of the function:
\[
f(1) = 3(1) + 2 = 3 + 2 = 5
\]
### Summary of Results:
- **(a)** \( f(-3) = 9 \)
- **(b)** \( f(0) = -3 \)
- **(c)** \( f(1) = 5 \)
Reviewed and approved by the UpStudy tutoring team
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Simplify this solution Extra Insights
To find the values of \( f(-3) \), \( f(0) \), and \( f(1) \): (a) Since \( -3 < 0 \), we use the first case of the piecewise function: \[ f(-3) = (-3)^2 = 9. \] (b) For \( f(0) \), since \( x = 0 \), we use the second case: \[ f(0) = -3. \] (c) For \( f(1) \), since \( 1 > 0 \), we use the third case: \[ f(1) = 3(1) + 2 = 5. \] So, the complete responses are: (a) \( f(-3) = 9 \) (b) \( f(0) = -3 \) (c) \( f(1) = 5 \)
