Work each problem. Find a function g(x)=ax+b whose graph can be o...

Question

Work each problem. Find a function g(x)=ax+b whose graph can be obtained by translating the graph of ƒ(x)=2x+5 up 2 units and to the left 3 units.

Accepted Answer

Suppose the graph of G FX equals C X plus D is obtained by translating the graph of F FX equals four X plus 7-Up four units. And to the left five units determine the function G FX. Possible answers being four, X plus 11, 4, X plus two, four, X plus 22 or four, X plus 31. Now, so this, let's take G X and instead it equals to all of our transformations. You have pets X. Now it says we're translating to the left by five units. So in our parentheses, we will add five to the X. We're also translating up by 40 units. So we will add four to the outside. So let's replace our F of X with our actual equation. We have four X plus five like so plus seven and then adding four at the end, we get four multiplied by X plus five plus 11. Now we can distribute our four to our X plus five, four multiplied by X and four multiplied by five. This gives us four X plus 20 plus 11, which finally gives us four X plus 31. We can't simplify anymore. So our answer corresponds to answer D OK. I hope to help you solve the problem. Thank you for watching. Goodbye.

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Work each problem. Find a function g(x)=ax+b whose graph can be obtained by translating the graph of ƒ(x)=2x+5 up 2 units and to the left 3 units.