If f(x)=x^2-1, describe in words what 5f(x)+3 would do to the graph of f(x).

Question

Help pretty please. It would be appreciated.

Answer 1

Let's start by thinking about the original function, f(x)=x²-1.

It will be a parabola with it's vertex at y=-1.

If we multiply it by 5, i.e., 5f(x), the resulting function will be 5f(x)=5(x²-1) or 5x²-5. The coefficient on x² will increase the slope while the constant, -5, will move the function's vertex to y=-5.

If we then add a constant, 3, to this new function, the resulting function will be 5f(x)+3 = 5x²-5+3 = 5x²-2.The coefficient on x² increases the slope while the new constant lowers the function's vertex to y=-2.

Therefore, the overall function shift:

1. Increases the slope of the function five times.
2. Moves the graph down by 1, moving it's vertex to y=-2.

Answer 2

The t coefficient will make the graph get bigger more quickly, i.e. it will be steeper.

The +3 moves the whole graph up so that the vertex will be at y=+2 instead of -1.