Question

choose the correct function/equation for the following description.
a linear function whose graph passes through the origin

choose the correct answer below.

a. $f(x)=5x$

b. $f(x)=3x + 6$

c. $f(x)= - 8$

d. $f(x)=x^2$

Explanation:

Step1: Recall linear function form

A linear function has the form \( f(x) = mx + b \), where \( m \) is the slope and \( b \) is the y - intercept. If the graph passes through the origin \((0,0)\), when \( x = 0 \), \( f(0)=0 \).

Step2: Analyze each option

• Option A: For \( f(x)=5x \), when \( x = 0 \), \( f(0)=5\times0 = 0 \). Also, it is in the form of a linear function (\( m = 5\), \( b = 0\)).
• Option B: For \( f(x)=3x + 6 \), when \( x = 0 \), \( f(0)=3\times0+6=6

eq0 \), so it does not pass through the origin.

• Option C: \( f(x)= - 8 \) is a constant function (a special case of linear function with \( m = 0\), \( b=-8\)). When \( x = 0 \), \( f(0)=-8

eq0 \), so it does not pass through the origin.

• Option D: \( f(x)=x^{2} \) is a quadratic function, not a linear function.

Answer:

A. \( f(x) = 5x \)