Question

5
select the correct answer from each drop - down menu.
the function f is given by the table of values as shown below.

x	1	2	3	4	5
f(x)	13	19	37	91	253

use the given table to complete the statements.
the parent function of the function represented in the table is
if function f was translated down 4 units, the - values would be
a point in the table for the transformed function would be

Explanation:

To solve this, we analyze the function from the table and apply transformations:

Step 1: Identify the Parent Function

First, we check the pattern of \( f(x) \). Let’s test \( f(x) = 3^x + 10 \) (or similar exponential behavior):

• For \( x=1 \): \( 3^1 + 10 = 13 \) (matches \( f(1)=13 \))
• For \( x=2 \): \( 3^2 + 10 = 19 \) (matches \( f(2)=19 \))
• For \( x=3 \): \( 3^3 + 10 = 37 \) (matches \( f(3)=37 \))
• For \( x=4 \): \( 3^4 + 10 = 91 \) (matches \( f(4)=91 \))
• For \( x=5 \): \( 3^5 + 10 = 253 \) (matches \( f(5)=253 \))

Thus, the parent function is \( \boldsymbol{3^x} \) (exponential function), since \( f(x) = 3^x + 10 \) is a transformation of \( 3^x \).

Step 2: Vertical Translation (Down 4 Units)

A vertical translation down 4 units affects the \( \boldsymbol{f(x)} \)-values (y-values) by subtracting 4. So new \( f(x) \)-values = original \( f(x) - 4 \).

Step 3: Transformed Function’s Point

Take a point from the table, e.g., \( (1, 13) \). After translation: \( 13 - 4 = 9 \), so the point becomes \( (1, 9) \).

Final Answers (Filling Drop-Downs):

1. The parent function: \( \boldsymbol{3^x} \) (or "exponential function" if options include it).
2. The values affected: \( \boldsymbol{f(x)} \) (y-values).
3. New \( f(x) \)-values: original \( f(x) - 4 \) (e.g., \( 13-4=9 \), \( 19-4=15 \), etc.).
4. A transformed point: \( \boldsymbol{(1, 9)} \) (or any \( (x, f(x)-4) \) from the table).

(Note: If drop-down options include specific choices, adjust to match. For example, if parent function options are "linear", "quadratic", "exponential", choose "exponential". For the translation, confirm the affected values are \( f(x) \)-values, and the new values are original minus 4. A sample point is \( (1, 9) \) from \( (1, 13) \) after subtracting 4.)

Answer:

To solve this, we analyze the function from the table and apply transformations:

Step 1: Identify the Parent Function

First, we check the pattern of \( f(x) \). Let’s test \( f(x) = 3^x + 10 \) (or similar exponential behavior):

• For \( x=1 \): \( 3^1 + 10 = 13 \) (matches \( f(1)=13 \))
• For \( x=2 \): \( 3^2 + 10 = 19 \) (matches \( f(2)=19 \))
• For \( x=3 \): \( 3^3 + 10 = 37 \) (matches \( f(3)=37 \))
• For \( x=4 \): \( 3^4 + 10 = 91 \) (matches \( f(4)=91 \))
• For \( x=5 \): \( 3^5 + 10 = 253 \) (matches \( f(5)=253 \))

Thus, the parent function is \( \boldsymbol{3^x} \) (exponential function), since \( f(x) = 3^x + 10 \) is a transformation of \( 3^x \).

Step 2: Vertical Translation (Down 4 Units)

A vertical translation down 4 units affects the \( \boldsymbol{f(x)} \)-values (y-values) by subtracting 4. So new \( f(x) \)-values = original \( f(x) - 4 \).

Step 3: Transformed Function’s Point

Take a point from the table, e.g., \( (1, 13) \). After translation: \( 13 - 4 = 9 \), so the point becomes \( (1, 9) \).

Final Answers (Filling Drop-Downs):

1. The parent function: \( \boldsymbol{3^x} \) (or "exponential function" if options include it).
2. The values affected: \( \boldsymbol{f(x)} \) (y-values).
3. New \( f(x) \)-values: original \( f(x) - 4 \) (e.g., \( 13-4=9 \), \( 19-4=15 \), etc.).
4. A transformed point: \( \boldsymbol{(1, 9)} \) (or any \( (x, f(x)-4) \) from the table).

(Note: If drop-down options include specific choices, adjust to match. For example, if parent function options are "linear", "quadratic", "exponential", choose "exponential". For the translation, confirm the affected values are \( f(x) \)-values, and the new values are original minus 4. A sample point is \( (1, 9) \) from \( (1, 13) \) after subtracting 4.)