If f left-parenthesis x right-parenthesis equals 2 superscript x baseline minus 10 and the domain of f left-parenthesis x right-parenthesis is the set of integers from negative 1 to 3, which values are elements of the range of f left-parenthesis x right-parenthesis? Select all that apply.
(2 points)
Responses
negative 12
Image with alt text: negative 12
negative 10
Image with alt text: negative 10
negative 9
Image with alt text: negative 9
negative 6
Image with alt text: negative 6
negative 2
Image with alt text: negative 2
To find the range of f(x), we substitute each value in the domain into the function and evaluate it.
f(-1) = 2^(-1) - 10 = 0 - 10 = -10
f(0) = 2^0 - 10 = 1 - 10 = -9
f(1) = 2^1 - 10 = 2 - 10 = -8
f(2) = 2^2 - 10 = 4 - 10 = -6
f(3) = 2^3 - 10 = 8 - 10 = -2
Therefore, the elements of the range of f(x) are -10, -9, -8, -6, and -2.
To find the range of the function f(x), we need to substitute the given values from the domain into the equation f(x) = 2^x - 10.
Let's substitute each value from the domain into the equation:
For x = -1:
f(-1) = 2^(-1) - 10
f(-1) = 1/2 - 10
f(-1) = -19.5
For x = 0:
f(0) = 2^(0) - 10
f(0) = 1 - 10
f(0) = -9
For x = 1:
f(1) = 2^(1) - 10
f(1) = 2 - 10
f(1) = -8
For x = 2:
f(2) = 2^(2) - 10
f(2) = 4 - 10
f(2) = -6
For x = 3:
f(3) = 2^(3) - 10
f(3) = 8 - 10
f(3) = -2
Therefore, the values that are elements of the range of f(x) are: -19.5, -9, -8, -6, and -2.