A function is a mathematical relationship that uniquely maps values of one set to the values of another set.

Checking and securing understanding of moving between function notation and the definition

Maths

Checking and securing understanding of function notation

Transforming graphs: y = f(x) + a

Transforming graphs: y = f(x + a)

Transforming graphs: y = −f(x)

Transforming graphs: y = f(−x)

Transforming graphs: y = af(x)

Transforming graphs: y = f(ax)

Transforming graphs: combinations of transformations

Problem solving with graph transformations

In this unit, function notation is used to describe various transformations. Pupils therefore need to be familiar with function notation which is introduced in the prior unit. 

In this unit pupils learn how to perform transformations on functions both algebraically and visually.

Transformations of graphs

Add 3 to the given value of $$x$$ then substitute into the function.

Evaluate the function for the given value of $$x$$ then add 3

Multiply $$x$$ by 3 then substitute this value into the function

Evaluate the function for the given value of $$x$$ then multiply by 3

Match up these manipulations of $$\text{f}(x)$$ to their definitions. 

If $$\text{g}(x)=3x-5$$ match up these manipulation to their value when $$x=3$$.

When $$\text{f}(x)=2x+4$$ which of these is an expression for $$\text{f}(x+3)$$?

When $$\text{f}(x)=x^2+4x$$ which of these is an expression for $$2\text{f}(x)$$?

When $$\text{f}(x)=5-3x$$ which of these is an expression for $$2\text{f}(x-4)$$?

When $$\text{f}(x)=2x-x^2$$ which of these is an expression for $$\text{f}(3x)-2$$?

A {{}} uniquely maps values from the domain to values in the range. 

If $$\text{f}(x)= 5x-4$$ what is the value of $$\text{f}(3)$$ ?

If $$\text{g}(x)= x^2- 3x$$ what is the value of $$\text{g}(4)$$ ?

If $$\text{f}(x) = 2x + 4$$ and $$\text{g}(x) = 3x- 2$$, what is an expression for $$\text{fg}(x)$$ ? 

Checking and securing understanding of moving between function notation and the definition

Lesson outcome