Question

3 multiple choice 1 point the graph of y = 3^x is labelled as ii. which is the graph of y = 3^x+3? 4 multiple choice 1 point consider the graph of y = |x|. what will be the effect on the graph if x is replaced with -x? a horizontal shift of 1 unit to the right no change a flip over the x - axis a horizontal shift of 1 unit to the left

Explanation:

Step1: Recall graph - shifting rule

For a function \(y = f(x)\), the graph of \(y=f(x)+k\) is a vertical - shift of the graph of \(y = f(x)\). If \(k>0\), the shift is \(k\) units up; if \(k < 0\), the shift is \(|k|\) units down.

Step2: Analyze the given functions

The function \(y = 3^{x}+3\) is of the form \(y=f(x)+3\) where \(f(x)=3^{x}\). Since \(k = 3>0\), the graph of \(y = 3^{x}+3\) is a vertical shift of the graph of \(y = 3^{x}\) 3 units up.
Looking at the graph, the graph of \(y = 3^{x}\) is labeled as II. The graph that is 3 units above II is V.

for the second question:

Step1: Recall function - transformation rule

For a function \(y = f(x)\), if we replace \(x\) with \(-x\), we get \(y = f(-x)\). The graph of \(y = f(-x)\) is the reflection of the graph of \(y = f(x)\) about the \(y\) - axis.
For the function \(y=|x|\), if we replace \(x\) with \(-x\), we have \(y = |-x|\). Since \(|-x|=|x|\) for all real - valued \(x\), the graph of \(y = |-x|\) is the same as the graph of \(y = |x|\).

Answer:

B. V