**Middle School Number Sense Lesson 72: Functions (with Exponents)**

Back in November, we introduced the concept of functions (

**Function**), and earlier this month we discussed function compositions (

**FunctionCompo**). But each time, we left out any mention of exponents. Today we will add that little bit of complexity. On average, today's concept shows up a little later on number sense tests, but also far more often. It appeared

**18 times**last year (on average, once per test), with a median placement at question #53. 8 times it was at

**question # 72**.

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In each of these examples, simply substitute in the given value of x to determine the function's output.

**Example 1:**

**If f(x) = 3x**

^{2}+ 4x + 1, then f(-2) = ___1. Substitute -2 for x.

2. 3(-2)

^{2}+ 4(-2) + 1 = 3(4) - 8 + 1 = 12 - 7 =

**5**.

**Example 2:**

**If f(x) = x**

^{2}- 11x + 14, then f(9) = ___1. Substitute 9 for x.

2. 9

^{2}- 11<9) + 14 = 81 - 99 + 14 =

**-4**.

**Example 3:**

**If f(x) = 18/x**

^{3}, then f(3) = ___ (fraction)1. Substitute 3 for x.

2. 18/3

^{3}= 18/27 =

**2/3**.

Example 4:

Example 4:

**If f(x) = √(11x + 4), then f(7) = ___**

1. Substitute 7 for x.

2. √(11 x 7 + 4) = √(77 + 4) = √81 =

**9**.

**Example 5:**

**If f(x) = 17x**

^{2}, then f(√5) = ___1. Substitute √5 for x.

2. 17(√5)

^{2}= 17(5) =

**85**.

**Example 6:**

**If f(x) = x**

^{2}- 2x + 1, then f(3.3) = ___1. This variety shows up often on high school tests. The secret is to recognize that

**x**is the square of the binomial

^{2}- 2x + 1**(x - 1)**. So substitute 3.3 for x in (x - 1)

^{2}.

2. (3.3 - 1)

^{2}= (2.3)

^{2}=

**5.29**.

**Check back soon for a free worksheet to help you practice FunctionExpo.**

**Up Next for Middle School: ProbDice**