Question

Evaluate the piecewise function at the given values of the independent variable.
f left parenthesis x right parenthesis equals
4 x plus 5
if x less than 0
3 x plus 7
if x greater than or equals 0
​(a) f left parenthesis negative 3 right parenthesis
​(b) f left parenthesis 0 right parenthesis
​(c) f left parenthesis 4 right parenthesis
Question content area bottom
Part 1
​(a) f left parenthesis negative 3 right parenthesisequals
  
enter your response here

Answer 1

To evaluate the piecewise function \( f(x) \):

1. **Function Definition**:
- \( f(x) = 4x + 5 \) if \( x < 0 \)
- \( f(x) = 3x + 7 \) if \( x \geq 0 \)

Now let's evaluate the function for each requested value.

### (a) \( f(-3) \)

Since \(-3 < 0\), we use the first part of the function:
\[
f(-3) = 4(-3) + 5 = -12 + 5 = -7
\]

So,
\[
f(-3) = -7
\]

### (b) \( f(0) \)

Since \(0 \geq 0\), we use the second part of the function:
\[
f(0) = 3(0) + 7 = 0 + 7 = 7
\]

So,
\[
f(0) = 7
\]

### (c) \( f(4) \)

Since \(4 \geq 0\), we use the second part of the function:
\[
f(4) = 3(4) + 7 = 12 + 7 = 19
\]

So,
\[
f(4) = 19
\]

### Summary of Results:
- \( f(-3) = -7 \)
- \( f(0) = 7 \)
- \( f(4) = 19 \)

If you need further assistance, feel free to ask!