# Question Video: Finding the Expression of a Function Transformation

Consider the function 𝑓(𝑥) = 𝑥² − 3𝑥 − 4. Find 𝑓(𝑥 + 3).

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### Video Transcript

Consider the function 𝑓 of 𝑥 equals 𝑥 squared minus three 𝑥 minus four. Find 𝑓 of 𝑥 plus three.

In order to find 𝑓 of 𝑥 plus three, we need to replace all of the 𝑥s with 𝑥 plus three. So essentially, we’re replacing 𝑥 with 𝑥 plus three and then evaluating. So here we can see we’ve replaced 𝑥 with 𝑥 plus three.

And now we need to evaluate this. 𝑥 plus three squared is 𝑥 plus three times 𝑥 plus three. And then we also need to distribute the negative three to the 𝑥 plus three in the middle. 𝑥 times 𝑥 is 𝑥 squared. 𝑥 times three is three 𝑥. Three times 𝑥 is three 𝑥. And three times three is nine.

And now we will distribute negative three to 𝑥 plus three. Negative three times 𝑥 is negative three 𝑥. And negative three times three is negative nine. And then we bring down our minus four.

So now we need to combine like terms. Our highest power is two. So 𝑥 squared needs to go first. Now we can combine all of the 𝑥s. Three 𝑥 plus three 𝑥 minus three 𝑥 is three 𝑥. And now for the numbers, the constants, nine, negative nine, and negative four make negative four. Therefore, 𝑓 of 𝑥 plus three is equal to 𝑥 squared plus three 𝑥 minus four.