Question

1. given the function, what is f(4)? type a response

Explanation:

Step1: Determine the equation of the line

First, find the slope \( m \) of the line. From the graph, we can see that the line passes through \((0, -1)\) (the y - intercept, \( b=-1\)) and another point, say \((2, 0)\). The slope formula is \( m=\frac{y_2 - y_1}{x_2 - x_1}\). Using \((x_1,y_1)=(0, - 1)\) and \((x_2,y_2)=(2,0)\), we get \( m=\frac{0 - (-1)}{2-0}=\frac{1}{2}\). So the equation of the line (function) is \( f(x)=mx + b=\frac{1}{2}x-1\).

Step2: Calculate \( f(4) \)

Substitute \( x = 4 \) into the function \( f(x)=\frac{1}{2}x-1\). So \( f(4)=\frac{1}{2}(4)-1\). First, calculate \(\frac{1}{2}(4) = 2\), then \( 2-1=1\).

Answer:

\( 1 \)