Graphs of Functions (AQA A-Level Mathematics): Quizzes

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Sketching Polynomials
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How many turning points can a quartic (degree 4) polynomial have?

Up to 3 turning points

Where does a positive quartic graph start and end?

Top left to top right

If the coefficient of x3x^3 is positive, where does the cubic graph start and end?

Bottom left to top right

For y=(x+1)(x+2)(x3)(x1)y = (x + 1)(x + 2)(x - 3)(x - 1), what is the y-intercept?

(0,6)(0, 6)

What happens to the curve at a double root?

The curve touches and turns around

What happens at a single root?

The curve crosses the x-axis

Which property describes y=x2y = x^2 at the origin?

It is flat at the origin

What are asymptotes on the graph of y = rac{1}{x}?

Lines it approaches but never touches

How does the graph y=x4y = x^4 compare to y=x2y = x^2?

Similar shape but steeper

What property describes y=sqrtxy = sqrt{x} at the origin?

It is vertical at the origin

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