Algebra - Function Notation

Function Notation

Algebra 1

Words to remember:

• Function: a relation in which each element of the domain (x-value) is mapped to (paired with) exactly one element of the range (y-value). Another way to look at it is each value of the independent variable maps to exactly one value for the dependent variable.

• Independent Variable: the variable in a function that represents the input values.

• Dependent Variable: the variable in a function that represents the output values.

• Continuous Graph: a graph in the coordinate plane that is made up of connected lines or curves with no breaks.

• Discrete Graph: a graph that has a finite or limited number of data points.

Function Notation

• Function Notation is the way a function is written.

• A precise way of giving information about a function without a long explanation.

• The most popular function notation is

   $f\left(x\right)$  (read f of x)

Function Notation

The meaning of f(x) is the output of the value of f when the input value is x.

Multiple Choice

f(x) means the same thing as ____.

• x

• t

• y

• r

Multiple Choice

Evaluate $g\left(a\right)=-2a-5$  at $a=4$  

• g(4)=13

• g(4)=3

• g(4)=-13

• g(4)=4

Multiple Choice

Which statement best describes the function h(t) = 210 – 15t?

• h is the function name; h(t) is the input, or independent variable; and t is the output, or dependent variable.

• h is the function name; t is the input, or independent variable; and h(t) is the output, or dependent variable.

• t is the function name; h(t) is the input, or independent variable; and h is the output, or dependent variable.

• t is the function name; h is the input, or independent variable; and h(t) is the output, or dependent variable.

Consider the equation:  

 $2y=x+1$  Write the equation using function notation where x is the independent variable.

•  $2y=x+1$  

•  $y=\frac{1}{2}x+\frac{1}{2}$    (divide both sides by 2)

•  $f\left(x\right)=\frac{1}{2}x+\frac{1}{2}$   (write the equation in function notation)

Multiple Choice

Consider the function represented by the equation 6c = 2p – 10. Write the equation in function notation, where c is the independent variable.

• $f\left(c\right)=\frac{1}{3}p+\frac{5}{3}$

• $f\left(c\right)=3c+5$

• $f\left(p\right)=\frac{1}{3}p+\frac{5}{3}$

• $f\left(p\right)=3c+5$

Multiple Choice

What is the value of x in:
f(3) = 2x + 1

• 3
• 2
• 1
• 0

Poll

Rate your level of understanding:

• 5 - I've got this!

• 4 - I understand for the most part and feel like I can work through the lesson.

• 3- I have a decent understanding, but still have some questions

• 2 - I am pretty confused, can we schedule a zoom meeting?

• 1 - I need help!