Question

On a coordinate plane, a straight line with a negative slope, labeled f of x, crosses the y-axis at (0, 4), and the x-axis at (4, 0).
Which is true regarding the graphed function f(x)?

f of 0 = 3
f of 5 = negative 1
f of 3 = 2
f of 2 = negative 2

Answer 1

To determine which of the given options is true for the function \( f(x) \), we first need to find the equation of the line.

Given:
- The line crosses the y-axis at \( (0, 4) \), which tells us the y-intercept \( b = 4 \).
- The line crosses the x-axis at \( (4, 0) \).

We know that the general form of a linear equation is \( y = mx + b \), where \( m \) is the slope and \( b \) is the y-intercept.

First, find the slope \( m \). The slope is calculated using the formula
\[ m = \frac{y_2 - y_1}{x_2 - x_1} \]
Using the points \( (0, 4) \) and \( (4, 0) \):
\[ m = \frac{0 - 4}{4 - 0} = \frac{-4}{4} = -1 \]

So the equation of the line is:
\[ y = -x + 4 \]

We can now find the values of \( f(x) \) for different \( x \) values based on this equation.

1. For \( f(0) \):
\[ f(0) = -0 + 4 = 4 \]
Therefore, \( f(0) \neq 3 \).

2. For \( f(5) \):
\[ f(5) = -5 + 4 = -1 \]
Therefore, \( f(5) = -1 \).

3. For \( f(3) \):
\[ f(3) = -3 + 4 = 1 \]
Therefore, \( f(3) \neq 2 \).

4. For \( f(2) \):
\[ f(2) = -2 + 4 = 2 \]
Therefore, \( f(2) \neq -2 \).

Thus, the only true statement regarding the graphed function \( f(x) \) is:
\[ f(5) = -1 \]