Graphs Of Functions Flashcards Preview

Math A Level > Graphs Of Functions > Flashcards

Flashcards in Graphs Of Functions Deck (16)
Loading flashcards...
1
Q

What graph equation can have many different shapes?

A

y=kx^n

2
Q

Y=kx^n when n is positive and even

A

You get a U shape if k is positive

You get an n shape when k is negative

3
Q

Y=kx^n when n is positive and odd

A

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

Negative k top left to bottom right vice Versa

4
Q

Y=kx^n when n is negative and even

A

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

K is negative the graph is bellow x axis.

5
Q

Y=kx^n when n is negative and odd

A

You get a graph with two bits opposite each other.

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

6
Q

What’s an asymptote of a curve

A

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

7
Q

Quartics are equations

A

With a x^4 term as the highest power

8
Q

Negative coefficient of x^4 in quartic graphs

Positive is the contrary

A

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

9
Q

Four main graph transformations

A

Y=f(x+c)

Y=f(x)+c

Y=af(x)

Y=f(ax)

10
Q

Y=f(x+c)

A

C>0

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

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

11
Q

Y=f(x)+c

A

C>0

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

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

12
Q

Y=af(x)

A

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

Page 31

13
Q

Y=f(ax)

A

Graph is squashed horizontally or stretched

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

Page 31

14
Q

When asked to do a combination of transformations remember to

A

Do them one at a time.

15
Q

graph equations

y = 2/x^2

Y= -1/x^4

Y= 3/x

Y= -1/x^3

A

Y = 2x^-2

Y = -x^-4

Y= 3x^-1

Y= -x^-3

16
Q

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

A

(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