Evaluating Functions

Hello! Today we are going to take a look at evaluating functions and expressions. All this requires is plugging in different values for variables and simplifying. Let’s start with a super simple example.

Evaluate the function \(f(x)=3x-7 \text{ at } x=6\).

To solve, start by plugging in 6 anywhere you see an \(x\).

\(f(6)=3(6)-7\)

 

Using parentheses helps you keep the operations straight; we know that we need to multiply 3 and 6.

Now, we were asked to evaluate the function at \(x=6\). When written in function notation like this, all we need to do is solve for \(f(6)\). So we just need to simplify the right side of the equation. Start by multiplying 3 and 6.

\(f(6)=18-7\)

 

Now, subtract.

\(f(6)=11\)

 

Let’s try another one.

Evaluate the function \(g(x)=2x^{2}+4x+1\) at \(x=-3\).

Don’t let the \(g(x)\) confuse you! Treat it just like you would if it were an \(f(x)\). Since we are evaluating at \(x=-3\), solve for \(g(-3)\).

Start by plugging in \(-3\) anywhere you see an \(x\).

\(g(-3)=2(-3)^{2}+4(-3)+1\)

 

Notice how important our parentheses are in our first term: \(2(-3)^{2}\). If we didn’t have them, it would look like this: \(2-3^{2}\). You would mistakenly subtract a positive number squared instead of multiplying by a negative number squared. So the parentheses are really important to keep our numbers straight.

Now that we’ve properly plugged in our value for \(x\), let’s simplify the expression by following the order of operations. First, simplify the exponents.

\(g(-3)=2(9)+4(-3)+1\)

 

Then, multiply.

\(g(-3)=18-12+1\)

 

And finally, add and subtract.

\(g(-3)=7\)

 

We’ve taken a look at evaluating functions. Now let’s take a look at evaluating expressions. In questions like these, we will follow the same steps we have been. The only difference is there will be more variables. Let’s try a problem.

Simplify the expression \(\frac{2x+3y}{z}\) when \(x=-4\), \(y=8\), and \(z=-2\).

First, plug in the given values for \(x\), \(y\), and \(z\). Make sure to use parentheses!

\(\frac{2(-4)+3(8)}{(-2)}\)

 

Now, simplify the expression. We will start by simplifying the numerator. First, multiply.

\(\frac{-8+24}{-2}\)

 

It’s okay that we dropped the parentheses in the denominator because -2 is the only term. Now, add -8 and 24.

\(\frac{16}{-2}\)

 

Remember, a fraction bar means division, so divide \(16\div (-2)=-8\).

Not too hard. Let’s try one last example together.

Simplify the expression \(\frac{2a}{b}-4c+d\) when \(a=9\), \(b=3\), \(c=-7\), and \(d=4\).

Start by substituting in the numbers.

\(\frac{2(9)}{3}-4(-7)+(4)\)

 

Now, simplify the expression. We’re going to start by multiplying.

\(\frac{18}{3}+28+4\)

 

Now we’re going to divide.

\(6+28+4\)

 

Finally, add these three numbers to get 38, which is your final answer.

I hope this video helped you better understand how to evaluate functions and expressions. Thanks for watching and happy studying!

 

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by Mometrix Test Preparation | This Page Last Updated: April 22, 2022