the graph of $y = f(x)$ is shown below. find the value of $f(1)$. answer attempt 1 out of 2 + additional…

Explanation:

Step1: Recall the meaning of ( f(1) )

To find ( f(1) ), we need to determine the ( y )-value of the function ( y = f(x) ) when ( x = 1 ). This means we look at the point on the graph of ( y = f(x) ) where the ( x )-coordinate is 1 and find the corresponding ( y )-coordinate.

Step2: Analyze the graph

Looking at the graph of the line ( y = f(x) ), we can see that it is a straight line. To find the value at ( x = 1 ), we can either use the equation of the line or directly observe the ( y )-value at ( x = 1 ) from the graph.

First, let's find the equation of the line. The line passes through the points ( (0, -3) ) (the ( y )-intercept) and ( (3, 0) ) (the ( x )-intercept). The slope ( m ) of the line is given by ( m=\frac{y_2 - y_1}{x_2 - x_1} ). Using the points ( (0, -3) ) and ( (3, 0) ): ( m=\frac{0 - (-3)}{3 - 0}=\frac{3}{3} = 1 )

So the equation of the line in slope-intercept form ( y=mx + b ) (where ( m ) is the slope and ( b ) is the ( y )-intercept) is ( y = 1x-3 ) or ( y=x - 3 ).

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

Alternatively, by looking at the graph, when ( x = 1 ), we can see that the ( y )-value is -2 (since the line passes through ( (1, -2) )).

Answer:

( -2 )