Fundamentals of Math

Fundamentals of Mathematics

4.3 Introduction to Functions Functions map sets of inputs into possible outputs, and each input can only correspond with a single output. They represent a relationship between constants and variables. In other words, it maps a number or variable to another unique number. For instance, if 3 is added to a number, then the sum produces a new value. Imagine if we applied this function to 5, we get the output of 8. Mathematically, this function is notated as: The value ( ) is an equation that assigns a single value of y for each number of . The input for the function ( ) is known as the independent variable (stands alone), while the output derived from this function is known as the dependent variable ( ). The domain is defined as all the possible values of the independent variable ( ) and range all the possible dependent variables ( ). Unless functions are used in context to real-world scenarios, the domain and range are usually (−∞, ∞) since any value can be input into a function and output returned. However, there are some exceptions. Remember when finding the domain: ( ) = + 3

• The denominator (bottom) of a fraction cannot be zero • The value under a square root sign must be positive

4.4 Evaluating Functions If you come across functions such as

= 2 2 − 5 + 7 , then you can re-write it using function

notation, = ( ) = 2 2 − 5 + 7 . Function notation is all about substitution. When a value is written in place of the in the function (i.e., (0) or (4) , then we evaluate the function at that specified value of .

(0) = 2(0) 2 − 5(0) + 7 = 0 − 0 + 7 = 7 (4) = 2(4) 2 − 5(4) + 7 = 32 − 20 + 7 = 19

Practice 4.4

Directions:

.

1.

( ) = 4 + 2 ; Find (3)

2.

( ) = 7 + 5 ; Find (−1)

2 + 4 + 3 ; Find ℎ(9)

3. ℎ( ) =

( ) = 3 2 − 7 + 1 ; Find (−2)

4.

Answer Key on Page 122

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