Question

find f(3).
$f(x)$ graph, $g(x) = 2x^2 - 5x - 4$, table for $h(x)$ with $x$ values -6, -4, -10, 1, -1 and corresponding $h(x)$ values 9, -4, 7, 5, 1

Explanation:

To find \( f(3) \), we analyze the graph of \( f(x) \):

Step 1: Identify the type of function \( f(x) \)

The graph of \( f(x) \) is a straight line, so \( f(x) \) is a linear function. We can find its equation using two points on the line. From the graph, we can see that the line passes through the points \( (0, -4) \) (the y - intercept) and \( (2, 0) \) (a point on the x - axis).

Step 2: Calculate the slope (\( m \)) of the line

The slope \( m \) of a line passing through two points \( (x_1,y_1) \) and \( (x_2,y_2) \) is given by the formula \( m=\frac{y_2 - y_1}{x_2 - x_1} \). Using the points \( (0,-4) \) and \( (2,0) \):
\[
m=\frac{0 - (-4)}{2-0}=\frac{4}{2} = 2
\]

Step 3: Write the equation of the line

The equation of a line in slope - intercept form is \( y=mx + b \), where \( m \) is the slope and \( b \) is the y - intercept. We know that \( m = 2 \) and \( b=-4 \) (from the point \( (0,-4) \)), so the equation of \( f(x) \) is \( f(x)=2x-4 \).

Step 4: Evaluate \( f(3) \)

Substitute \( x = 3 \) into the equation \( f(x)=2x - 4 \):
\[
f(3)=2(3)-4=6 - 4=2
\]

Answer:

\( f(3)=2 \)