Video: Finding the Expression of a Function Transformation

Consider the function 𝑓(π‘₯) = π‘₯Β² βˆ’ 3π‘₯ βˆ’ 4. Find 𝑓(π‘₯ + 3).

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Video Transcript

Consider the function 𝑓 of π‘₯ equals π‘₯ squared minus three π‘₯ minus four. Find 𝑓 of π‘₯ plus three.

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

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

And now we will distribute negative three to π‘₯ plus three. Negative three times π‘₯ is negative three π‘₯. 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 π‘₯ squared needs to go first. Now we can combine all of the π‘₯s. Three π‘₯ plus three π‘₯ minus three π‘₯ is three π‘₯. And now for the numbers, the constants, nine, negative nine, and negative four make negative four. Therefore, 𝑓 of π‘₯ plus three is equal to π‘₯ squared plus three π‘₯ minus four.

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