Question

31 select all exponential functions: a $y = \frac{3}{2}x + 3$ b $y = 3 \cdot (2)^x$ c $f(x) = .5 \cdot (3)^x$ d $y = 3x$ e $f(x) = 2 \cdot (2)^x$ f $f(x) = 4.5$

Explanation:

Step1: Recall Exponential Function Form

An exponential function has the form \( y = a \cdot b^x \), where \( a
eq 0 \), \( b > 0 \), and \( b
eq 1 \), and \( x \) is the exponent.

Step2: Analyze Option A

\( y=\frac{3}{2}x + 3 \) is a linear function (form \( y = mx + b \)), not exponential.

Step3: Analyze Option B

\( y = 3 \cdot (2)^x \) matches \( y = a \cdot b^x \) ( \( a = 3 \), \( b = 2 \) ), so it's exponential.

Step4: Analyze Option C

\( f(x)=0.5 \cdot (3)^x \) matches \( y = a \cdot b^x \) ( \( a = 0.5 \), \( b = 3 \) ), so it's exponential.

Step5: Analyze Option D

\( y = 3x \) is linear (form \( y = mx \)), not exponential.

Step6: Analyze Option E

\( f(x)=2 \cdot (2)^x \) matches \( y = a \cdot b^x \) ( \( a = 2 \), \( b = 2 \) ), so it's exponential.

Step7: Analyze Option F

\( f(x)=4.5 \) is a constant function, not exponential.

Answer:

B. \( y = 3 \cdot (2)^x \), C. \( f(x) = 0.5 \cdot (3)^x \), E. \( f(x) = 2 \cdot (2)^x \)