GCSE(F),

A **sketch** of a function will show the *x* and *y* axes and a minimum amount of data, such as where the function cross the *x*- and *y*-axes. When more than one function is plotted on the same graph, the different functions must be identified. A scale does not need to be provided:

The equation of a linear function can be determined from a sketch by determining the gradient and intercept points.

1. Sketch the function *y* = -3*x* - 4.

Answer:

The -3*x* indicates a negative gradient, and falls from left to right. The - 4 indicates that one of the coordinates is (0, -4).

Set *y* to 0 and solve for x; i.e. 0 = -3*x* - 4 therefore *x*= -1.33 (2dp).

2. What are the intersection points for *y* = 3*x* + 6 on the *x* and *y* axis?

Answer: (-2, 0) and (0, 6)

Set *y* = 0: 0 = 3*x* + 6, therefore *x* = -2. Coordinate is (-2, 0).

Set *x* = 0: *y* = 3(0) + 6, therefore *y* = 6. Coordinate is (0, 6).

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