Question

exponential functions
match the exponential function with the correct “family member.”
drag all of the exponential functions to the correct family member.

y = 0.5(3)^x

y = 2(3)^x

y = 5^x

y = 3^x

y = 5·5^x

y = -5^x

y = -2(3)^x

parent

stretch

shrink

reflection

Explanation:

Step1: Identify Parent Functions

Parent exponential functions have the form \( y = a^x \) where \( a>0, a
eq1 \) and no vertical/horizontal stretches, shrinks, or reflections (coefficient of \( a^x \) is 1, no negative sign). So \( y = 3^x \) (base 3) and \( y = 5^x \) (base 5) are parents.

Step2: Identify Stretch Functions

A vertical stretch occurs when the coefficient of \( a^x \) is \( >1 \). For \( y = 5 \cdot 5^x \), coefficient 5 > 1 (stretch of \( y = 5^x \)). For \( y = 2(3)^x \), coefficient 2 > 1 (stretch of \( y = 3^x \)).

Step3: Identify Shrink Functions

A vertical shrink occurs when the coefficient of \( a^x \) is between 0 and 1. For \( y = 0.5(3)^x \), coefficient 0.5 (0 < 0.5 < 1) shrinks \( y = 3^x \).

Step4: Identify Reflection Functions

A reflection over the x - axis occurs when there is a negative sign in front of the exponential term. For \( y = -5^x \), negative sign reflects \( y = 5^x \). For \( y = -2(3)^x \), negative sign reflects \( y = 2(3)^x \).

Answer:

• Parent: \( y = 3^x \), \( y = 5^x \)
• Stretch: \( y = 5 \cdot 5^x \), \( y = 2(3)^x \)
• Shrink: \( y = 0.5(3)^x \)
• Reflection: \( y = -5^x \), \( y = -2(3)^x \)