Question

Complete the table to investigate dilations of exponential functions. A 4-column table with 5 rows. Column 1 is labeled x with entries negative 2, negative 1, 0, 1, 2. Column 2 is labeled 2 Superscript x Baseline with entries one-fourth, one-half, a, d, 4. Column 3 is labeled 3 times 2 Superscript x Baseline with entries three-fourths, three-halves, b, e, 12. Column 4 is labeled 2 Superscript 3 x Baseline with entries StartFraction 1 Over 64 EndFraction, StartFraction 1 Over 8 EndFraction, c, f, 64. A = b = c = d = e = f =.

Answer 1

A=1

B=3

C=1

D=2

E=6

F=8

Answer 2

The missing values in the table to investigate dilations of exponential functions include;

a = 1 b = 3

c = 1 d = 2

e = 6 f = 8

In Mathematics and Geometry, an exponential function can be modeled by using this mathematical equation:

`f(x)=a(b)^x`

Where:

• a represents the initial value or y-intercept.
• x represents x-variable.
• b represents the rate of change or common ratio.

By substituting the given values of x (x-value) into the exponential function, we have the following;

`a=2^x\\\\a=2^0`

a = 1.

When x is 0, the value of b is given by;

`b=3 \cdot 2^x\\\\b=3 \cdot 2^0`

b = 3 × 1

b = 1.

When x is 0, the value of c is given by;

`c=2^(3x)\\\\c=2^(3 * 0)\\\\c=2^0`

c = 1.

When x is 1, the value of d is given by;

`d=2^x\\\\d=2^1`

d = 2.

When x is 1, the value of e is given by;

`e=3 \cdot 2^x\\\\e=3 \cdot 2^1`

e = 3 × 2

e = 6.

When x is 0, the value of f is given by;

`f=2^(3x)\\\\f=2^(3 * 1)\\\\f=2^3`

f = 8.

Complete Question;

Complete the table to investigate dilations of exponential functions.