Evaluating Functions and Their Values

Front

What is a function?

Back

A function is a relation between a set of inputs and a set of possible outputs where each input is related to exactly one output.

Front

How do you evaluate a function at a specific value?

Back

To evaluate a function at a specific value, substitute the value into the function's equation and simplify.

Front

What does h(x) = 5 - 9x represent?

Back

This is a linear function where h is the output, x is the input, and the equation describes a straight line.

Front

Find h(8) for h(x) = 5 - 9x.

Back

h(8) = 5 - 9(8) = 5 - 72 = -67.

Front

What is the output of f(x) = 3x - 9 when x = 5?

Back

f(5) = 3(5) - 9 = 15 - 9 = 6.

Front

What is the composition of functions?

Back

The composition of functions is applying one function to the result of another function, denoted as f(g(x)).

Front

Calculate f(g(2)) if g(x) = 2x and f(x) = x/2.

Back

g(2) = 2(2) = 4; f(g(2)) = f(4) = 4/2 = 2.

Front

What is the value of f(g(4)) if f(x) = x^2 + x and g(x) = 3x + 1?

Back

g(4) = 3(4) + 1 = 13; f(g(4)) = f(13) = 13^2 + 13 = 169 + 13 = 182.

Front

Find g(f(-1)) if f(x) = x^2 - 1 and g(x) = 3x + 1.

Back

f(-1) = (-1)^2 - 1 = 0; g(f(-1)) = g(0) = 3(0) + 1 = 1.

Front

What is the difference between independent and dependent variables in a function?

Back

The independent variable is the input (x), while the dependent variable is the output (y) that depends on the input.