Question

Classify the function f left parenthesis x right parenthesis equals Start Fraction 3 x plus 4 over 8 End Fraction as linear, quadratic, exponential, or none of these.
(1 point)
Responses

linear
linear

quadratic
quadratic

exponential
exponential

none of these

Answer 1

To classify the function \( f(x) = \frac{3x + 4}{8} \), we first simplify it.

The function can be rewritten as:

\[
f(x) = \frac{3x}{8} + \frac{4}{8} = \frac{3}{8}x + \frac{1}{2}
\]

This is in the form \( f(x) = mx + b \), where:
- \( m = \frac{3}{8} \) (the slope)
- \( b = \frac{1}{2} \) (the y-intercept)

Since this is a linear equation, we classify the function as linear.

So the correct response is:

**linear**