Proportional Function Math Example 4

Follow the full solution, then compare it with the other examples linked below.

Example 4

medium
Explain why f(x)=3x+2f(x) = 3x + 2 is NOT a proportional function, and find the value of bb that would make g(x)=3x+bg(x) = 3x + b proportional.

Solution

  1. 1
    f(x)=3x+2f(x)=3x+2 has a non-zero yy-intercept. Check: f(0)=2โ‰ 0f(0)=2 \neq 0. For proportionality, y/xy/x must be constant: f(1)/1=5f(1)/1=5, f(2)/2=4f(2)/2=4. Not constant. Not proportional.
  2. 2
    For g(x)=3x+bg(x)=3x+b to be proportional, we need g(0)=0g(0)=0, i.e., b=0b=0. Then g(x)=3xg(x)=3x satisfies g(x)/x=3g(x)/x=3 (constant).

Answer

f(x)=3x+2f(x)=3x+2 is not proportional; b=0b=0 makes g(x)=3xg(x)=3x proportional
Proportional functions must pass through the origin. Any non-zero yy-intercept means the ratio y/xy/x changes with xx, violating proportionality. Linear functions with bโ‰ 0b \neq 0 are affine, not proportional.

About Proportional Function

A proportional function has the form f(x)=kxf(x) = kx for a constant kโ‰ 0k \neq 0 โ€” it passes through the origin and the ratio f(x)/x=kf(x)/x = k is constant.

Learn more about Proportional Function โ†’

More Proportional Function Examples

Example 1 easy

The weight of water is proportional to its volume. [formula] liters weighs [formula] kg. Write the f

Example 2 medium

Determine whether [formula] is proportional to [formula] given the table: [formula] and [formula]. I

Example 3 easy

Hooke's Law states spring force is proportional to stretch: [formula]. If [formula] N when [formula]

โ† All Proportional Function Examples Proportional Function Concept