Question

If f(x)= x^2- 1, describe in words what the following would do to the graph of f(x):

1. f(x)-4
2. f(x-4)
3. -f(x+2)
4. 5f(x)+3
5. f(2x)
6. |f(x)|

Answer 1

f(x)+a shifts up a units (or down if a<0)

f(x-c) shift horizontally c units right (or left if c<0)

-f(x) reflects over the x-axis

af(x) stretches/shrinks by a factor of a (stretch if |a|>1, shrink if |a|<1)

f(bx) horizontally stretches/shrinks

|f(x)| think of as a piecewise function.
.....|f(x)|=f(x) where f(x)> or =0
.....|f(x)|=-f(x) where f(x)<0 (see above, this would be a reflection)