Question

question 1 of 3
select the correct answer from each drop-down menu.
the function f is given by this table of values.

x	f(x)
0	48
1	24
2	12
3	6

use this table to complete the statements.
the parent function of the function represented in the table is exponential .
if function f is vertically compressed by a factor of $\frac{1}{4}$, the f(x) -values will be
multiplied by 4
decreased by 4
increased by 4
divided by 4
a point in the table for the transformed function is (1,6)

Explanation:

1. First, confirm the parent function type: as x increases by 1, f(x) is multiplied by $\frac{1}{2}$ (e.g., $96 \times \frac{1}{2}=48$, $48 \times \frac{1}{2}=24$), which follows the pattern of an exponential function $f(x)=a(b)^x$.
2. A vertical compression by a factor of $\frac{1}{4}$ means every output value of the original function is scaled by $\frac{1}{4}$, which is equivalent to dividing each f(x)-value by 4.
3. Verify the transformed point: for the original point (1,24), applying the vertical compression gives $24 \times \frac{1}{4}=6$, so the transformed point is (1,6).

Answer:

The parent function of the function represented in the table is exponential.
If function $f$ is vertically compressed by a factor of $\frac{1}{4}$, the $f(x)$-values will be divided by 4.
A point in the table for the transformed function is (1,6)