2.6

Graphs of functions

9 flashcards to master Graphs of functions

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Definition Flip

What are the coordinates of the origin?

Answer Flip

The origin is the point where the x-axis and y-axis intersect. Its coordinates are (0, 0).

Key Concept Flip

Sketch the general shape of a quadratic graph. What is its equation form?

Answer Flip

A quadratic graph is a parabola (U-shaped). The general form of a quadratic equation is y = ax² + bx + c, where a, b, and c are constants.

Key Concept Flip

What is the shape of a reciprocal graph and what is its equation?

Answer Flip

A reciprocal graph has two curves, approaching the x and y axis but never touching them. Its equation form is y = k/x, where k is a constant.

Definition Flip

What is an asymptote? Give an example in the context of graphs.

Answer Flip

An asymptote is a line that a curve approaches but never touches.

Example: the graph of y = 1/x has asymptotes at x = 0 and y = 0.
Key Concept Flip

Describe the general shape of an exponential graph, where y=a^x and a > 1.

Answer Flip

An exponential graph rises rapidly as x increases and approaches the x-axis as x decreases. It always passes through the point (0,1) and has the x-axis (y=0) as an asymptote.

Key Concept Flip

Describe the general shape of a cubic graph.

Answer Flip

A cubic graph generally has an 'S' shape or a similar wavy form. Its equation form is y = ax³ + bx² + cx + d, where a, b, c, and d are constants.

Definition Flip

What is the x-intercept of a graph? How do you find it?

Answer Flip

The x-intercept is the point where the graph crosses the x-axis. To find it, set y = 0 in the equation and solve for x.

Definition Flip

What is the y-intercept of a graph? How do you find it?

Answer Flip

The y-intercept is the point where the graph crosses the y-axis. To find it, set x = 0 in the equation and solve for y.

Key Concept Flip

Explain how to plot the graph of y = 2x + 1.

Answer Flip

Create a table of values for x and y. For each x-value, calculate the corresponding y-value using the equation. Then, plot the points (x, y) on a coordinate plane and draw a straight line through them.

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2.5 Quadratics 2.7 Straight line graphs

Key Questions: Graphs of functions

What are the coordinates of the origin?

The origin is the point where the x-axis and y-axis intersect. Its coordinates are (0, 0).

What is an asymptote? Give an example in the context of graphs.

An asymptote is a line that a curve approaches but never touches.

Example: the graph of y = 1/x has asymptotes at x = 0 and y = 0.
What is the x-intercept of a graph? How do you find it?

The x-intercept is the point where the graph crosses the x-axis. To find it, set y = 0 in the equation and solve for x.

What is the y-intercept of a graph? How do you find it?

The y-intercept is the point where the graph crosses the y-axis. To find it, set x = 0 in the equation and solve for y.

About Graphs of functions (2.6)

These 9 flashcards cover everything you need to know about Graphs of functions for your Cambridge IGCSE Mathematics (0580) exam. Each card is designed based on the official syllabus requirements.

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