Question

1. fill in the blanks using the available answer choices.

determine whether the equation $y = \frac{1}{x} - 4$ represents a linear or nonlinear function. explain.
the equation \underline{(blank 1)} be written in the form $y = mx + b$, so it is \underline{(blank 2)}.
blank 1 options

• can
• cannot

blank 2 options

• linear
• nonlinear

Explanation:

Step1: Recall linear function form

A linear function is in the form \( y = mx + b \), where \( m \) (slope) and \( b \) (y - intercept) are constants, and \( x \) is to the first power. The given equation is \( y=\frac{1}{x}-4=x^{- 1}-4 \). Here, the exponent of \( x \) is - 1, not 1. So it cannot be written in the form \( y = mx + b \).

Step2: Determine function type

Since the equation cannot be written in the linear function form \( y=mx + b \), it is a nonlinear function.

Answer:

Blank 1: cannot
Blank 2: nonlinear