Question

Can you please help me? I don't know how to solve this problem! Please explain your steps!!! Thanks in advance! :)

The graph of g(x) is the graph of f(x) = x2 shifted 4 units left, vertically stretched by a factor of 3, then shifted 5 units up. What is the function rule for g(x)?

Answer 1

Start visually. Draw the original function. Then 1) draw (or imagine or draw a dotted line function) 4 units to the left. That part should be straightforward. 2) Stretching vertically means that every y value will be amplified by 3. That is, 3 times more (higher) for positive values, and 3 times more negative for the negatives. 3)Just like you did in step 1, a shift, but this time each y value is 5 greater.

Answer 2

There are a couple of ways to get the new function rule. Either from the new graph, which a lot of prople find to be the easiest, or algebraically. Either way gets you the same answer. Try the graph first because it shows a lot.