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 is transformed by a horizontal translation in the opposite direction
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
f$$(x)+5$$ is a translation of $$+5$$ in the $$y$$-direction so pupils may assume that f$$(x+5)$$ is a translation of $$+5$$ in the $$x$$-direction.
Visually showing pupils, using graphing technology, that f$$(x+5)$$ is not a translation to the right will help. Showing them a comparison of the two tables of values for both functions shows them why this happens.
Licence
Lesson video
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Prior knowledge starter quiz
6 Questions
Q1.$$\text{f}(x)+a$$ is a of the graph of $$\text{f}(x)$$.
Q2.Match each piece of function notation to a description.
$$\text{f}(x)+4$$ -Â The output of $$\text{f}(x)$$ has $$4$$ added to it.
$$\text{f}(x+4)$$ -Â The input has $$4$$ added to it before the function is applied.
$$4\text{f}(x)$$ -Â The output of $$\text{f}(x)$$ is multiplied by $$4$$
$$\text{f}(x)-4$$ -Â The output of $$\text{f}(x)$$ has $$4$$ subtracted from it.
$$\text{f}(x-4)$$ -Â The input has $$4$$ subtracted before the function is applied.
Q3.Shape 'a' has been transformed to shape 'b' by translation of __________.
Q4.The transformation of the point $$(3,-2)$$ to the position $$(-4,-2)$$ could be described by __________.
Q5.The point $$(-1,13)$$ is translated $$+8$$ in the $$x$$-direction. What is its new position?
Q6.The point $$(c,-d)$$ is translated by $$9$$ in the negative $$x$$-direction. What is its new position?
Assessment exit quiz
6 Questions
Q1.$$\text{f}(x+a)$$ is a transformation by __________.
Q2.$$\text{f}(x+a)$$ is a transformation by translation of __________.
Q3.$$y=\text{f}(x)$$ is graphed. Which of these images shows the transformation $$y=\text{f}(x-3)$$?
Q4.$$y=\text{f}(x)$$ is graphed here. Which coordinate pairs will be on the transformation $$y=\text{f}(x+6)$$?
Q5.$$y=\text{f}(x)$$ is graphed. What transformation can we see graphed? $$y=$$
Q6.$$y=\text{f}(x)$$ is graphed here. Which could the graph of the transformation be?
