Chapter 7

Question 1

Continuous Function

Answer 1

A function that has no limits of breaks

Can be drawn without lifting the pen

Question 2

Formula of a hyperbola

Answer 2

y=k/x

Question 3

What type of function is a hyperbola

Answer 3

inverse function

Question 4

y asymptote of hyperbola

Answer 4

x -> ∞

Question 5

x asymptote of hyperbola

Answer 5

y -> ∞

Question 6

Transformed hyperbola formula

Answer 6

y=k/(bx+c)

Question 7

Formula of an absolute value

Answer 7

|x|{ (x if x≥0), (-x if x<0)

Question 8

Transformed absolute value formula

Answer 8

f(x) = |x - h| + k

Question 9

|x|≤ a

Answer 9

-a≤x≤a

Question 10

|x| ≥ a

Answer 10

x≤-a x≥a

Question 11

Transformations of a circle formula

Answer 11

(x-a)²+(y-b)²=r²

Question 12

How is the circle function created

Answer 12

using pythag, y is the distance of one side of a right angle triange to a point on a circle, x is the distance of the other, and the radius is the length of the hypotenuse

Question 13

y=-f(x)

Answer 13

reflect over x axis

Question 14

y=f(-x)

Answer 14

reflect over y axis

Question 15

Combined functions

Answer 15

f(x)+g(x)
f(x)-g(x)
f(x) * g(x)
f(x)/g(x)

etc…

Question 16

Composite functions

Answer 16

f(g(x)

the output of one function becomes the input of the outer function

Question 17

Steps of a reciprocal function

Answer 17

1) any point where f(x)=0, 1/f(x) has a verticle asymptote
2) any point where f(x)=±1, 1/f(x)=f(x)
3) as f(x)->0, 1/f(x) -> ∞ and as f(x) -> ∞, 1/f(x) -> 0
4) all turning points for f(x) become turning point 1/f(x)