Graphs Of Functions

Question 1

What graph equation can have many different shapes?

Answer 1

y=kx^n

Question 2

Y=kx^n when n is positive and even

Answer 2

You get a U shape if k is positive

You get an n shape when k is negative

Question 3

Y=kx^n when n is positive and odd

Answer 3

You get corner to corner shape (look on page 30)

Negative k top left to bottom right vice Versa

Question 4

Y=kx^n when n is negative and even

Answer 4

You get a graph with two bits next to each other )|(

K is negative the graph is bellow x axis.

Question 5

Y=kx^n when n is negative and odd

Answer 5

You get a graph with two bits opposite each other.

If k is negative graph is in top left and bottom right.

Question 6

What’s an asymptote of a curve

Answer 6

A line which the curve gets infinitely close to, but never touches.

Question 7

Quartics are equations

Answer 7

With a x^4 term as the highest power

Question 8

Negative coefficient of x^4 in quartic graphs

Positive is the contrary

Answer 8

Curve slopes downwards (is negative) for very positive and negative x-values

Question 9

Four main graph transformations

Answer 9

Y=f(x+c)

Y=f(x)+c

Y=af(x)

Y=f(ax)

Question 10

Y=f(x+c)

Answer 10

C>0

F(x+c) f(x) shifted by c to the left

F(x-c) f(x) shifted by c to right

Question 11

Y=f(x)+c

Answer 11

C>0

f(x)+c is f(x) shifted c Upwards

F(x)-c is f(x) shifted c downwards

Question 12

Y=af(x)

Answer 12

A<0 graph is reflected in the x axis.
Squashes or stretches graph vertically depending on the number you use for a

Page 31

Question 13

Y=f(ax)

Answer 13

Graph is squashed horizontally or stretched

If a<0 the graph is also reflected in the y axis

Page 31

Question 14

When asked to do a combination of transformations remember to

Answer 14

Do them one at a time.

Question 15

graph equations

y = 2/x^2

Y= -1/x^4

Y= 3/x

Y= -1/x^3

Answer 15

Y = 2x^-2

Y = -x^-4

Y= 3x^-1

Y= -x^-3

Question 16

When x(x-2)^2(x+1) are factors

Answer 16

(X-2) is a double root so the curve touches the x axis at x=2

The curve crosses the x axis at x=0 and x=-1