Functions Theory (9th grade)

Question 1

What is a function’s domain?

Answer 1

All fo the possible x-values the function could have.

Question 2

What is a function’s range?

Answer 2

All of the possible y-values a function could have.

Question 3

How can you show that a graph is a function?

Answer 3

You use the vertical line test. That means, you imagine drawing all possible vertical lines on the graph. If any vertical line would intersect the function more than once, it’s not a function.

Question 4

How is the domain and range of a function related to the domain and range of the inverse?

Answer 4

• The domain of the original function is the range of the inverse.
• The range of the original function is the domain of the inverse.

Question 5

How do you shift f(x)=x² to the right by h?

Answer 5

You put a “-h” in with the x term.

g(x)=(x-h)²

Question 6

How do you shift f(x)=x² to the up by k?

Answer 6

You put a “+k” at the end.

g(x)=x²+k

Question 7

How do you mirror f(x)=x²+k over the x-axis?

Answer 7

You multiply the whole function by -1.

g(x)= -(x²+k).

Question 8

How do you mirror f(x)=x²+k over the y-axis?

Answer 8

You multiply the x-part by -1.

g(x)=(-x)²+k.

Question 9

How do you vertically stretch f(x)=x²+k by a?

Answer 9

You multiply the whole function by a.

g(x)=a(x²+k).

Question 10

How do you horizontally stretch f(x)=(x-h)²+k by b?

Answer 10

You multiply the whole x-part by a.

g(x)=(b(x-h))²+k.

Question 17

Where is the vertex and line of symmetry for

f(x)=a(b(x-h)²+k)?

Answer 17

Vertex: (h, a•k)

Line of symmetry: x=h