EDEXCEL A-LEVEL PURE MATHS (4): GRAPHS & TRANSFORMATIONS

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Last updated 4:26 PM on 6/29/26
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21 Terms

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What is a cubic function?

- A cubic function has the form ax³ + bx² + cx + d, where a, b, c and d are real numbers and a is non-zero.

- The graph of a cubic function can take several different forms depending on the exact nature of the function.

- If 'p' is a root of the function f(x), then the graph of y = f(x) touches or crosses the x-axis at the point (p, 0).

- You can sketch the graph of a cubic function by finding the roots of the function.

<p>- A cubic function has the form ax³ + bx² + cx + d, where a, b, c and d are real numbers and a is non-zero.</p><p>- The graph of a cubic function can take several different forms depending on the exact nature of the function.</p><p>- If 'p' is a root of the function f(x), then the graph of y = f(x) touches or crosses the x-axis at the point (p, 0).</p><p>- You can sketch the graph of a cubic function by finding the roots of the function.</p>
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What are some examples of sketching graphs of a cubic function?

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What are some more examples of sketching graphs of a cubic function?

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What are even more examples of sketching graphs of a cubic function?

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What is a quartic function?

- A quartic function has the form f(x) = ax⁴ + bx³ + cx² + dx + e, where a, b, c, d and e are all real numbers and a is non-zero.

- The graph of a quartic function can take several different forms, depending on the exact nature of the function.

- You can sketch the graph of a quartic function by finding the roots of the function.

<p>- A quartic function has the form f(x) = ax⁴ + bx³ + cx² + dx + e, where a, b, c, d and e are all real numbers and a is non-zero.</p><p>- The graph of a quartic function can take several different forms, depending on the exact nature of the function.</p><p>- You can sketch the graph of a quartic function by finding the roots of the function.</p>
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What are some examples of sketching graphs of a quartic function?

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How can you sketch graphs of reciprocal functions?

You can sketch graphs of reciprocal functions such as y = 1/x, y = 1/x² and y = -2/x by considering their asymptotes.

<p>You can sketch graphs of reciprocal functions such as y = 1/x, y = 1/x² and y = -2/x by considering their asymptotes.</p>
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What are some examples of sketching graphs of reciprocal functions?

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How can you sketch curves of functions to show points of intersection and solutions to equations?

The x-coordinate(s) at the point of intersection of the curves with equations y = f(x) and y = g(x) are the solution(s) to the equation f(x) = g(x).

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What are some examples of sketching curves of functions to find points of intersection and solutions to equations?

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What are some more examples of sketching curves of functions to find points of intersection and solutions to equations?

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What are even more examples of sketching curves of functions to find points of intersection and solutions to equations?

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How can you transform graphs?

- By altering the function.

- Adding or subtracting a constant 'outside' the function translates a graph vertically.

- The graph of y = f(x) + a is a translation of the graph y = f(x) by the vector (0 a).

- Adding or subtracting a constant 'inside' the function translates the graph horizontally.

- The graph of y = f(x + a) is a translation of the graph y = f(x) by the vector (-a 0).

<p>- By altering the function.</p><p>- Adding or subtracting a constant 'outside' the function translates a graph vertically.</p><p>- The graph of y = f(x) + a is a translation of the graph y = f(x) by the vector (0 a).</p><p>- Adding or subtracting a constant 'inside' the function translates the graph horizontally.</p><p>- The graph of y = f(x + a) is a translation of the graph y = f(x) by the vector (-a 0).</p>
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What are some examples of transformations of graphs?

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What are some more examples of transformations of graphs?

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What are some examples of transformations of graphs with asymptotes?

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How can you strech graphs?

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What are some examples of streching graphs?

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What are some more examples of streching graphs?

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How can you reflect graphs, and what is an example of a reflection of a graph?

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EDEXCEL A-LEVEL PURE MATHS CHAPTER FOUR: GRAPHS & TRANSFORMATIONS

(MAKE SURE YOU KNOW THE FOLLOWING)

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