# Evaluating Functions Assignment Algebra 1

### David W.

Round Rock, TX

I️ don’t know how to do this

H(a)=a2+5a; find h(8)

Feb 5 | Tiffany from Winslow, AR | 1 Answer | 0 Votes

Evaluating Functions### Kenneth S.

Mesa, AZ

how would be find the answer to f(g(x)) when f(x)=2x-12 , g(x)=x^2+2x+4, f(x)=-3/2x-6

f(x)=2x-12 , g(x)=x2+2x+4, f(x)=-3/2x-6

Oct 7 | Katie from Centreville, VA | 1 Answer | 0 Votes

Evaluating Functions### Michael J.

East Elmhurst, NY

Find the initial amount injected and the amount in the bloodstream after 7 hours. Round your answers to the nearest hundredth as necessary

The number of milligrams D(h) of a drug in a patient's bloodstream h hours after the drug is injected is modeled by the following function. D(h)=25e^-0.3h

Apr 15 | Asterly from Pompano Beach, FL | 1 Answer | 0 Votes

Evaluating Functions### Kenneth S.

Mesa, AZ

Evaluate the problem

If A?B=A^2+AB+B^2, evaluate 4?3

8/24/2016 | Lillianah from Cleveland, OH | 2 Answers | 0 Votes

Evaluating Functions### Michael J.

East Elmhurst, NY

Find and simplify: f(-x) - f(x) for the given function of f

f(x)= 5x^3 + 6x^2 - 3x - 17 I have tried this problem many times and cannot seem to get the correct answer. Please help! Thanks!

10/20/2015 | Erin from East Lansing, MI | 1 Answer | 0 Votes

FunctionsEvaluating Functions### Michael F.

Wilton, CT

Find and simplify the difference quotient

Find and simplify the difference quotient: f(x+h) - f(x) / h, where h cannot = 0, for the function: f(x)= 3x2 - x +2 Have tried this multiple times and still get the same answer...

10/20/2015 | Erin from East Lansing, MI | 1 Answer | 0 Votes

FunctionsEvaluating Functions### Bruce Y.

Cincinnati, OH

Evaluate the function at the given values of the independent variable and simplify.

f(x)= (3x)/(11*lxl) (That's the absolute value of x) f(r^8) I don't understand how you get the answers after plugging in r^8 in the equation

FunctionsEvaluating Functions### Mark M.

Carson, CA

Evaluate enter only the sum

S21for 23+20+17+14+.....

4/7/2015 | Kyrsten from Fort Wayne, IN | 1 Answer | 0 Votes

Algebra 2HelpfulEvaluating FunctionsSequencesMath### Phillip R.

North Providence, RI

how do i evaluate this function?

k(n)=3n-4; find k(-2-n)

8/26/2014 | Rylee from Cheyenne, WY | 1 Answer | 0 Votes

Algebra 2Evaluating Functions### Philip P.

Olney, MD

how do i evaluate this function?

g(x) =3x-3 Find g(6)

8/26/2014 | Rylee from Cheyenne, WY | 1 Answer | 0 Votes

Algebra 2Evaluating Functions## Evaluating Functions

## Evaluating Functions

To evaluate a function is to:

Replace (substitute) its variable with a given number or expression.

Like in this example:

### Example: evaluate the function **f(x) = 2x+4** for **x=5**

Just replace the variable "x" with "5":

f(5) = 2×5 + 4 = 14

Answer: **f(5) = 14**

## More Examples

Here is a function:

f(x) = 1 − x + x^{2}

Important! The "x" is just a place-holder! And "f" is just a name.

These are all the **same function**:

- f(x) = 1 − x + x
^{2} - f(q) = 1 − q + q
^{2} - w(A) = 1 − A + A
^{2} - pumpkin(θ) = 1 − θ + θ
^{2}

### Evaluate For a Given Value:

Let us evaluate that function for x=3:

f(3) = 1 − 3 + 3^{2} = 1 − 3 + 9 = **7**

### Evaluate For a Given Expression:

Evaluating can also mean replacing with an expression (such as **3m+1** or **v ^{2}**).

Let us evaluate the function for x=1/r:

f(1/r) = 1 − (1/r) + (1/r)^{2}

Or evaluate the function for x = a−4:

f(a−4) = 1 − (a−4) + (a−4)^{2}

= 1 − a + 4 + a^{2} − 8a + 16

= 21 − 9a + a^{2}

## Another Example

You can use your ability to evaluate functions to find other answers:

### Example: h(x) = 3x^{2} + ax − 1

- You are told that
**h(3) = 8**, can you work out what "a" is?

First, evaluate h(3):h(3) = 3×(3)^{2} + a×3 − 1

Simplify:h(3) = 27 + 3a − 1

h(3) = 26 + 3a

Now ... we know that **h(3) = 8**, so: 8 = 26 + 3a

Swap sides:26 + 3a = 8

Subtract 26 from both sides:3a = −18

Divide by 3:a = −6

Check: h(3) = 3(3)^{2} − 6×3 − 1 = 27 − 18 − 1 = 8

## Careful!

I recommend putting the substituted values inside parentheses **()** , so you don't make mistakes.

### Example: evaluate the function **h(x) = x**^{2} + 2 for **x = −3**

^{2}+ 2

Replace the variable "x" with "−3":

h(−3) = **(−3)**^{2} + 2 = **9 **+ 2 = **11**

Without the () you could make a mistake:

h(−3) = **−3 ^{2 }**+ 2 =

**−9**+ 2 =

**−7**(WRONG!)

Also be careful of this:

**f(x+a)** is not the same as **f(x) + f(a)**

### Example: g(x) = x^{2}

g(w+1) = (w+1)^{2} = **w ^{2} + 2w + 1**

*vs*

g(w) + g(1) = w^{2} + 1^{2} = **w ^{2} + 1**

Different Result!

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