Graphs And Transformations

Question 1

What happens if p is a root of the function f(x)

Answer 1

The graph of y=f(x) touches or crosses the x-axis at the point (p,0)

Question 2

Which two graphs have asymptotes at x = 0 and y = 0

Answer 2

The graphs of:

Question 3

What is the solution to the equation f(x) = g(x)

Answer 3

The solution is the x coordinates at the point of intersection of the curves with equations y = f(x) and y = g(x)

Question 4

What graph is left after a translation of the graph y = f(x) by the vector (0 a)

Answer 4

The graph of y = f(x) + a

Question 5

What graph is left after a translation of the graph y = f(x) by the vector (-a 0)

Answer 5

The graph of y = f(x + a)

Question 6

When you translate a function what happens to any asymptotes

Answer 6

Any asymptotes are also translated

Question 7

What graph do you get when you stretch the graph y = f(x) by a scale factor of a in the vertical direction

Answer 7

The graph of y = af(x)

Question 8

What graph do you get when you stretch the graph y = f(x) by a scale factor of 1 / a in the horizontal direction

Answer 8

The graph of y = f(ax)

Question 9

What graph do you get when you reflect the graph of y = f(x) in the x-axis

Answer 9

The graph of y = -f(x)

Question 10

What graph do you get when you reflect the graph of y = f(x) in the y-axis

Answer 10

The graph of y = f(-x)