Solving Functions (Function Notation)

Front

What is function notation?

Back

Function notation is a way to represent a function using symbols. It typically uses the letter 'f' followed by the variable in parentheses, such as f(x), where 'x' is the input value.

Tags

CCSS.8.F.A.1

CCSS.HSF.IF.A.1

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 in place of the variable. For example, to evaluate f(x) = 2x + 3 at x = 4, calculate f(4) = 2(4) + 3 = 11.

Tags

CCSS.HSF.IF.A.2

Front

What does it mean for a function to be linear?

Back

A linear function is a function that can be graphically represented as a straight line. It has the form f(x) = mx + b, where m is the slope and b is the y-intercept.

Tags

CCSS.8.F.B.4

CCSS.HSF.LE.A.2

Front

What is the slope of a linear function?

Back

The slope of a linear function is a measure of how steep the line is. It is calculated as the change in the y-value divided by the change in the x-value (rise/run).

Tags

CCSS.8.EE.B.5

Front

What is the y-intercept of a function?

Back

The y-intercept of a function is the point where the graph of the function crosses the y-axis. It occurs when x = 0.

Front

How do you find the x-intercept of a function?

Back

To find the x-intercept of a function, set f(x) = 0 and solve for x. The x-intercept is the point where the graph crosses the x-axis.

Front

What is the difference between independent and dependent variables?

Back

The independent variable is the input of a function (often x), while the dependent variable is the output (often f(x)). The value of the dependent variable depends on the value of the independent variable.

Tags

CCSS.6.EE.C.9

Front

What is a function's domain?

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 a function's range?

Back

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

Front

How do you solve for x in a function equation?

Back

To solve for x in a function equation, isolate x on one side of the equation using algebraic operations. For example, in f(x) = 2x + 3, to find x when f(x) = 7, set 7 = 2x + 3 and solve for x.

Tags

CCSS.HSF.IF.A.2