Question

score: 11/30 penalty: 1 off
question
watch video show examples
find the value of f(-7).
y = f(x)
answer attempt 1 out of 2
submit answer

Explanation:

Step1: Identify the line for \( x = -7 \)

The left - most part of the graph \( y = f(x) \) is a straight line. We need to find the equation of this line to determine \( f(-7) \). First, find two points on this line. From the graph, when \( x = 0 \), \( y = 2 \) (the y - intercept), and when \( x = 2 \), \( y = 0 \) (the x - intercept).

Step2: Calculate the slope of the line

The slope \( m \) of a line passing through two points \( (x_1,y_1)=(0,2) \) and \( (x_2,y_2)=(2,0) \) is given by the formula \( m=\frac{y_2 - y_1}{x_2 - x_1} \). Substituting the values, we get \( m=\frac{0 - 2}{2 - 0}=\frac{-2}{2}=- 1 \).

Step3: Write the equation of the line

Using the slope - intercept form \( y=mx + b \), where \( m=-1 \) and \( b = 2 \) (the y - intercept), the equation of the line is \( y=-x + 2 \).

Step4: Substitute \( x=-7 \) into the equation

Substitute \( x=-7 \) into \( y=-x + 2 \). We have \( y=-(-7)+2=7 + 2=9 \). So \( f(-7)=9 \).

Answer:

\( 9 \)