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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
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Part 1
​(a) f left parenthesis negative 3 right parenthesisequals
  
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1 answer

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!