Pure- Graphs and transformations (4) Flashcards

1
Q

What is the form of a cubic equation?

A

f(x)=ax^3 + bx^2 + cx + d

where a,b,c,d are real numbers and a isn’t 0

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2
Q

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

A

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

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3
Q

What is the form a quartic equation?

A

f(x)=ax^4 + bx^3 +cx^2 + dx + e

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4
Q

What are the asymptotes of y=k/x and y=k/x^2 where k is a real constant?

A

x=0

y=0

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5
Q

What is an asymptote?

A

A line which the graph approaches but never reaches.

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6
Q

What are the x-coordinates to the intersections of y=f(x) and y=g(x)?

A

The solutions to f(x)=g(x)

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7
Q

What transformation does y=f(x)+a correspond to ?

A

A translation of y=f(x) by a units vertically

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8
Q

What transformation does y=f(x+10) correspond to?

A

A translation of y=f(x) by -a units horizontally

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9
Q

What does the transformation y=af(x) correspond to?

A

A vertical stretch of y=f(x) by scale factor a

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10
Q

What does the transformation y=f(ax) correspond to?

A

A horizontal stretch of y=f(x) by scale factor 1/a

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11
Q

What does the transformation y=-f(x) correspond to?

A

A reflection of y=f(x) in the x-axis

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12
Q

What does the transformation y=f(-x) correspond to?

A

A reflection of y=f(x) in the y-axis

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