Question

grade 8 algebra unit 2 lesson 9
ready, set, go
ready
compare different characteristics of each type of function by filling in the cells of each
table as completely as possible.
1

1. find the y - intercepts for the following equations.

a. ( y = 3x )
b. ( y = 3^{x} )

Explanation:

Step1: Recall the formula for y - intercept

The y - intercept of a function \(y = f(x)\) is found by setting \(x = 0\). For a linear function \(y=mx + b\), when \(x = 0\), \(y=b\). For an exponential function \(y = a\cdot b^{x}\), when \(x = 0\), \(y=a\cdot b^{0}=a\) (since \(b^{0}=1\) for \(b
eq0\)).

Step2: Find the y - intercept for \(y = 3x\)

Set \(x = 0\) in \(y=3x\). Then \(y=3\times0 = 0\).

Step3: Find the y - intercept for \(y = 3^{x}\)

Set \(x = 0\) in \(y = 3^{x}\). Then \(y=3^{0}=1\) (using the rule \(a^{0}=1\) for \(a
eq0\)).

Answer:

a. The y - intercept of \(y = 3x\) is \(0\).
b. The y - intercept of \(y = 3^{x}\) is \(1\).