Level 4 · Mathematics M4.10
Functions and graphs
Use function notation, learn the shapes of the main graphs, and move them about.
Planned. This book is not written yet. Below is its plan, which a teacher can already use.
You are ready for this book if
You can draw the graph of y = x² − 4 from a table of values.
- One step up M5.1 Functions, polynomials and the binomial
- This book M4.10 Functions and graphs
- One step down M3.9 Coordinates and straight lines
The plan
- M4.10.1 Function notation
- Find f(3) when f(x) = 2x − 1
- Solve f(x) = 7 for the same function
- M4.10.2 Composite and inverse functions
- Find fg(x) from two functions f and g
- Find the inverse function f⁻¹(x)
- M4.10.3 Cubic, reciprocal and circle graphs
- Sketch y = x³ and y = 1/x
- Sketch the circle x² + y² = 25
- Match an equation to the shape of its graph
- M4.10.4 Exponential graphs
- Draw y = 2ˣ from a table of values
- Tell a growth curve from a decay curve
- M4.10.5 Graphs of sin, cos and tan
- Sketch y = sin x and y = cos x up to 360°
- Use a graph to find two angles with sin x = 0.5
- M4.10.6 Moving graphs
- Sketch y = f(x) + a and y = f(x + a)
- Sketch y = −f(x) and y = f(−x)
- M4.10.7 Gradients and areas under graphs
- Estimate the gradient of a curve by drawing a tangent
- Estimate the area under a curve using trapeziums
- Explain what gradient and area mean on a speed time graph
- M4.10.8 Solving with graphs and trials
- Solve an equation by finding where two graphs meet
- Find a root between two numbers by trying values
For parents and teachers
Level 4 fits learners who can already: follow a written argument. use letters for numbers. In many schools that is about 14 to 16, but start wherever the learner is.
Strand: Algebra. Written and drawn by attnom. Free to read, print and share.