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

To evaluate a function means to calculate the output value for a given input by substituting the input into the function's equation.

Front

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

Back

f(1) = 2(1) + 3 = 5.

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 (y-values) that the function can produce.

Front

How do you find f(2) if f(x) = x^2 + 3?

Back

f(2) = 2^2 + 3 = 4 + 3 = 7.

Front

What is the significance of the x-intercept of a function?

Back

The x-intercept is the point where the graph of the function crosses the x-axis, indicating where the function's output is zero.

Front

If f(x) = x^2 - 4, what are the x-intercepts?

Back

The x-intercepts are x = -2 and x = 2, where f(x) = 0.

Front

What does it mean for a function to be quadratic?

Back

A quadratic function is a polynomial function of degree 2, typically in the form f(x) = ax^2 + bx + c.

Front

How do you evaluate f(4) for f(x) = 3x^2 - 2x + 1?

Back

f(4) = 3(4)^2 - 2(4) + 1 = 48 - 8 + 1 = 41.