Question

the value of a graphed function doubles for each increase of 1 in the value of (x). which of the following could be the parent function of the graphed function?

• (y = 2^x)
• (y = x^2)
• (y = |2x|)
• (y = sqrt{x})

Explanation:

⚡ Using what you learned: Graphing Exponential Functions

Step 1: Analyze the growth pattern

The problem states that the value of the function doubles for each increase of \(1\) in the value of \(x\). This means:

$$f(x+1) = 2 \cdot f(x)$$

This constant multiplicative rate of change represents exponential growth with a base of \(2\).

Step 2: Identify the matching parent function

An exponential function with a base of \(2\) has the general form:

$$y = a \cdot 2^x$$

The parent function for this family of curves is:

$$y = 2^x$$

Answer:

\(y = 2^x\)