Question

unit 6 formative
6.3 formative (2 sides)
does the table represent a linear, or an
a.

x	0	1	2	3
y	8	4	2	1

Explanation:

Step1: Calculate the differences in y-values

For a linear function, the difference in \( y \)-values (slope) should be constant when \( x \) increases by 1. Let's find the differences between consecutive \( y \)-values.
From \( x = 0 \) to \( x = 1 \): \( 4 - 8 = -4 \)
From \( x = 1 \) to \( x = 2 \): \( 2 - 4 = -2 \)
From \( x = 2 \) to \( x = 3 \): \( 1 - 2 = -1 \)

Step2: Analyze the differences

In a linear function, the rate of change (slope) should be constant. Here, the differences between consecutive \( y \)-values are \( -4, -2, -1 \), which are not constant. Now, let's check if it's exponential. For an exponential function, the ratio of consecutive \( y \)-values should be constant.
From \( x = 0 \) to \( x = 1 \): \( \frac{4}{8} = 0.5 \)
From \( x = 1 \) to \( x = 2 \): \( \frac{2}{4} = 0.5 \)
From \( x = 2 \) to \( x = 3 \): \( \frac{1}{2} = 0.5 \)
The ratio of consecutive \( y \)-values is constant (\( 0.5 \)), so the function is exponential.

Answer:

The table represents an exponential function.