Question

The function f is defined as follows for the domain given.

f(x) = 2–2x domain = (-1,0, 1, 2}
Write the range of f using set notation. Then graph f.

Answer 1

The range of the function in ascending order is:

Range R = {-2, 0, 2, 4}

Explanation:

Given the function

f(x) = 2-2x

We know that the domain of the function is the set of input or arguments for which the function is real and defined.

In other words,

• Domain refers to all the possible sets of input values on the x-axis

As the domain of the function is given such as

Domain D = {-1, 0, 1, 2}

Determining the range

We also know that range is the set of values of the dependent variable for which a function is defined.

In other words,

Range refers to all the possible sets of output values on the y-axis.

As the domain is

Domain D = {-1, 0, 1, 2}

FOR x = 1

substitute x = -1 in the function

f(x) = 2-2x

f(-1) = 2-2(-1) = 2+2=4

so

at x = -1, y = 4

FOR x = 0

substitute x = 0 in the function

f(x) = 2-2x

f(-1) = 2-2(0) = 2-0=2

so

at x = 0, y = 2

FOR x = 1

substitute x = 1 in the function

f(x) = 2-2x

f(-1) = 2-2(1) = 2-2=0

so

at x = 1, y = 0

FOR x = 2

substitute x = 2 in the function

f(x) = 2-2x

f(-1) = 2-2(2) = 2-4=-2

so

at x = 2, y = -2

Thus combining all the output or y values correspond to the given input values, we get the range of the function.

Thus, the range of the function in ascending order is:

Range R = {-2, 0, 2, 4}