Evaluating Functions (Equations & Graphs)

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

What does it mean to evaluate a function?

Back

Evaluating a function means substituting a specific value for the variable in the function's equation to find the corresponding output.

Front

If f(x) = 4x + 7, what is f(3)?

Back

f(3) = 4(3) + 7 = 12 + 7 = 19.

Front

How do you find the x-value when f(x) = k?

Back

To find the x-value when f(x) = k, set the function equal to k and solve for x.

Front

What is the value of x when f(x) = 10 for f(x) = 2x?

Back

x = 5, since 2x = 10 implies x = 10/2.

Front

What is the vertex of a quadratic function?

Back

The vertex of a quadratic function in the form f(x) = ax^2 + bx + c is the point (h, k) where h = -b/(2a) and k = f(h).

Front

If f(x) = 2x^2 + 5x - 3, what is f(-1)?

Back

f(-1) = 2(-1)^2 + 5(-1) - 3 = 2 - 5 - 3 = -6.

Front

What does the graph of a function represent?

Back

The graph of a function represents all the ordered pairs (x, f(x)) where x is in the domain of the function.

Front

What is the domain of a function?

Back

The domain of a function is the set of all possible input values (x-values) for which the function is defined.

Front

What is the range of a function?

Back

The range of a function is the set of all possible output values (f(x) values) that the function can produce.