Evaluating Functions Revision Notes for Junior Cert Mathematics

Evaluating Functions

In this section, we will learn how to evaluate functions, which means finding the output of a function when you are given a specific input. This is a very common task in algebra, and it's simpler than it might seem at first!

What Does Evaluating a Function Mean?

When we evaluate a function, we are simply finding the value of the function for a specific input. For example, if we have a function $f(x)$ , evaluating the function for $x = 2$ means finding the value of $f(2)$ .

Steps to Evaluate a Function

Let's break down the steps you need to follow to evaluate a function, using examples along the way.

Step 1: Understand the Function

First, look at the function you are given. For example, consider the function:

$f(x) = 2x^2 + 3$

This function tells us that for any input $x$ , you need to square the input, multiply by 2, and then add 3 to find the output.

Step 2: Replace $x$ with the Input Value

Once you know what input you need to use (e.g., $x = 3$ ), substitute that number in place of $x$ in the function.

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Important Tip: Everywhere you see $x$ in the function, swap it with $3$ because you are substituting $x = 3$ . This is how you evaluate the function for the specific input.

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Example: To find $f(3)$ , replace $x$ with $3$ : $f(3) = 2(3)^2 + 3$

Step 3: Perform the Calculations

After substituting the input, follow the steps to calculate the output.

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Example: Now, calculate the value:

First, square the input: $3^2 = :highlight[9]$
Then, multiply by $2$ : $2 \times 9 = :highlight[18]$
Finally, add $3$ : $18 + 3 = :success[21]$ So, $f(3) = :success[21]$ .

After you've done the calculations, write down the output value. In this case:

$f(3) = :success[21]$

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Another Example Let's go through another example with a different function.

Function:

$g(x) = 4x - 5$

Input:

This time, let's find $g(2)$ .

Step 1: Replace $x$ with $2$ :

$g(2) = 4(2) - 5$

Step 2: Remember, everywhere you see $( x )$ , you're now swapping it with $2$ .

Step 3: Perform the calculations:

First, multiply: $4 \times 2 = :highlight[8]$
Then, subtract 5: $8 - 5 = :success[3]$

So, $g(2) = :success[3]$ .

Finally, write down the output value:

$g(2) = :success[3]$

Key Points to Remember

Always replace $x$ with the input value carefully: Make sure you substitute the correct value for $x$ and perform the operations in the right order.
Check your work: It's always a good idea to double-check your calculations to make sure you haven't made any mistakes.

By following these steps and practising, you'll be able to evaluate any function with confidence. Keep practising, and soon it will become second nature!

Evaluating Functions (Junior Cert Mathematics): Revision Notes