Question

1. identify the function family for each function.

a. $f(x) = 3x^2 - 4$
b. $g(x) = 2^x$
c. $h(x) = -2x - 5$
(handwritten text: use graphic organizers in book)

Explanation:

Part a: Analyze \( f(x) = 3x^2 - 4 \)

Step1: Recall function families. A quadratic function has the form \( f(x)=ax^2 + bx + c \) (\( a
eq0 \)).
Here, \( a = 3 \), \( b = 0 \), \( c=-4 \), so it matches the quadratic form.

Part b: Analyze \( g(x) = 2^x \)

Step1: Recall function families. An exponential function has the form \( f(x)=a\cdot b^x \) (\( a
eq0 \), \( b>0, b
eq1 \)).
Here, \( a = 1 \), \( b = 2 \), so it matches the exponential form.

Part c: Analyze \( h(x) = -2x - 5 \)

Step1: Recall function families. A linear function has the form \( f(x)=mx + b \) (\( m
eq0 \)).
Here, \( m=-2 \), \( b=-5 \), so it matches the linear form.

Answer:

a. Quadratic Function Family
b. Exponential Function Family
c. Linear Function Family