Question

use the graph below to answer the question.
which function is best represented by the graph?
a $f(x) = \frac{1}{8}x + 3$
b $f(x) = \frac{1}{8}x - 3$
c $f(x) = -8x + 3$
d $f(x) = -\frac{1}{8}x - 3$
e $f(x) = 8x - 3$

Explanation:

Step1: Analyze the slope and y-intercept

The general form of a linear function is \( f(x) = mx + b \), where \( m \) is the slope and \( b \) is the y-intercept. From the graph, we can see that the line is decreasing (going from top - left to bottom - right), so the slope \( m \) should be negative. Also, let's check the y - intercept. The line crosses the y - axis below the origin, so \( b\) is negative.

Step2: Evaluate each option

• Option A: \( f(x)=\frac{1}{8}x + 3\). The slope \( \frac{1}{8}\) is positive (line should be increasing) and \( b = 3\) is positive (y - intercept above origin). Eliminate A.
• Option B: \( f(x)=\frac{1}{8}x-3\). The slope \( \frac{1}{8}\) is positive (line should be increasing). Eliminate B.
• Option C: \( f(x)=- 8x + 3\). The slope \( - 8\) is negative, but \( b = 3\) is positive (y - intercept above origin). Eliminate C.
• Option D: \( f(x)=-\frac{1}{8}x-3\). The slope \( -\frac{1}{8}\) is negative (line is decreasing) and \( b=-3\) is negative (y - intercept below origin). This matches the graph's characteristics.
• Option E: \( f(x)=8x - 3\). The slope \( 8\) is positive (line should be increasing). Eliminate E.

Answer:

D. \( f(x)=-\frac{1}{8}x - 3\)