Functions and graphs
Build and connect the representations and methods in functions and graphs.
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Before you begin
Build and connect the representations and methods in functions and graphs.
Learning goals
- Read and plot ordered coordinate pairs
- Interpret and draw graphs of functions
- Find and interpret a graph gradient
Syllabus statements covered
- Cartesian coordinates in two dimensions • graph of a set of ordered pairs as a representation of a relationship between two variables • linear functions (y = ax + b) and quadratic functions (y = ax² + bx + c) • graphs of linear functions • the gradient of a linear graph as the ratio of the vertical change to the horizontal change (positive and negative gradients) • graphs of quadratic functions and their properties: - positive or negative coefficient of x^2 - maximum and minimum points - symmetry • sketching the graphs of quadratic functions given in the form: - y = (x − p)² + q - y = − (x − p)² + q - y = (x − a)(x − b) - y = − (x − a)(x − b) • graphs of power functions of the form y = ax^n, where n = −2, −1, 0, 1, 2, 3, and simple sums of not more than three of these • graphs of exponential functions y = ka^x, where a is a positive integer • estimation of the gradient of a curve by drawing a tangent
- Cartesian coordinates in two dimensions
- graph of a set of ordered pairs as a representation of a relationship between two variables
- linear functions y = ax + b
- graphs of linear functions
- the gradient of a linear graph as the ratio of the vertical change to the horizontal change (positive and negative gradients)
- quadratic functions y = ax^2 + bx + c
- graphs of quadratic functions and their properties: • positive or negative coefficient of x^2 • maximum and minimum points • symmetry
- sketching the graphs of quadratic functions given in the form: • y = (x − p)² + q • y = −(x − p)² + q • y = (x − a)(x − b) • y = −(x − a)(x − b)
- graphs of power functions y = ax^n , where n = −2, −1, 0, 1, 2, 3, and simple sums of not more than three of these
- graphs of exponential functions y = ka^x , where a is a positive integer, a > 1
- estimation of the gradient of a curve by drawing a tangent
Lessons
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- Coordinates, lines and gradientsG3 Mathematics 2027 · Express Secondary 1 Mathematics 2020Plot ordered pairs and read a straight line’s gradient from changes in the labelled coordinates.
- Quadratic graphs and turning pointsG3 Mathematics 2027 · Express Secondary 2 Mathematics 2021Use tables and symmetry to locate a quadratic curve’s roots and extremum.
- Sketch quadratics from their formG3 Mathematics 2027 · Express Secondary 3–4 Mathematics 2022Read a vertex or roots from a suitable form and locate the remaining features before sketching.
- Power and exponential graphsG3 Mathematics 2027 · Express Secondary 3–4 Mathematics 2022Use domains, tables and asymptotes to distinguish power functions from exponential growth.
- Estimate a curve’s gradientG3 Mathematics 2027 · Express Secondary 3–4 Mathematics 2022Draw a tangent at the specified point and use two separated points on that tangent.
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