Question

the graph of $y = f(x)$ is shown below. find the value of $f(1)$. answer attempt 1 out of 2 + additional solution - no solution

Explanation:

Step1: Determine the equation of the line

The graph is a straight line, so we can use the slope-intercept form \( y = mx + b \), where \( m \) is the slope and \( b \) is the y-intercept. From the graph, the y-intercept \( b = -3 \). To find the slope, we can use two points. Let's take the y-intercept \( (0, -3) \) and the x-intercept \( (3, 0) \). The slope \( m = \frac{0 - (-3)}{3 - 0} = \frac{3}{3} = 1 \). So the equation of the line is \( y = x - 3 \).

Step2: Find \( f(1) \)

Since \( f(x) = y = x - 3 \), substitute \( x = 1 \) into the equation: \( f(1) = 1 - 3 = -2 \).

Answer:

\( -2 \)