Transforming graphs: y = f(x) + a
I can recognise the effect of applying the transformation y = f(x) + a to a graph.
- Year 11
Transforming graphs: y = f(x) + a
I can recognise the effect of applying the transformation y = f(x) + a to a graph.
Lesson details
Key learning points
- Desmos is an effective tool for showing the effects of this transformation
- The actual function itself does not need to be known
- The graph of the function is transformed by a vertical translation
Keywords
Function - A function is a mathematical relationship that uniquely maps values of one set to the values of another set.
Transformation - A transformation is a process that may change the size, orientation or position of a shape or graph.
Common misconception
Pupils may not see the vertical translation depending on the function used to show the effect of $$a$$.
Ensure pupils consider a range of functions so that they can see the movement of the graph.
Licence
Prior knowledge starter quiz
6 Questions
Q1.When every point of a shape moves the same distance in the same direction the transformation is called a...
Q2.Match each piece of function notation to a description.
$$\text{f}(x)+11$$ -Â The output of $$\text{f}(x)$$ has $$11$$ added to it.
$$\text{f}(x+11)$$ -Â The input has $$11$$ added to it before the function is applied.
$$11\text{f}(x)$$ -Â The output of $$\text{f}(x)$$ is multiplied by $$11$$
$$\text{f}(x)-11$$ -Â The output of $$\text{f}(x)$$ has $$11$$ subtracted from it.
$$\text{f}(x-11)$$ -Â The input has $$11$$ subtracted before the function is applied.
Q3.Shape 'a' has been transformed to shape 'b' by a translation of...

Q4.For the function $$\text{f}(x)$$, $$\text{f}(8)=37$$, match these transformations of the function to their values.
$$\text{f}(8)+3$$ -Â $$40$$
$$3\text{f}(8)$$ -Â $$111$$
$$\text{f}(8)-3$$ -Â $$34$$
$$-3\text{f}(8)$$ -Â $$-111$$
$$3\text{f}(8)-3$$ -Â $$108$$
Q5.The point $$(4,1)$$ is translated 'up $$5$$'. What is it's new position?
Q6.The point $$(-5,-a)$$ is translated 'down $$4$$'. What is it's new position?
Assessment exit quiz
6 Questions
Q1.$$\text{f}(x)+a$$ is a transformation by...
Q2.$$\text{f}(x)+a$$ translates the graph by $$a$$ in the...
Q3.$$y=\text{f}(x)$$ is graphed here. The second line represents what transformation of $$y=\text{f}(x)$$?

Q4.$$y=\text{f}(x)$$ is graphed here. Which coordinate pairs will be on the transformation $$y=\text{f}(x)-6$$?
