Transforming graphs: y = f(−x)
I can recognise the effect of applying the transformation y = f(−x) to a graph.
- Year 11
Transforming graphs: y = f(−x)
I can recognise the effect of applying the transformation y = f(−x) 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 reflection in the y axis
Keywords
Transformation - A transformation is a process that may change the size, orientation or position of a shape.
Common misconception
Pupils mix-up $$-$$f$$(x)$$ and f$$(-x)$$. Which is a reflection in the $$x$$-axis? Which is in the $$y$$-axis?
f$$(-x)$$ is the input being multiplied by $$-1$$ before the function is applied. Which coordinate is the input? The $$x$$ coordinates change from positive to negative so this must be a reflection in the $$y$$ axis.
Licence
Lesson video
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Prior knowledge starter quiz
6 Questions
Q1.$$-\text{f}(x)$$ transforms the graph of $$\text{f}(x)$$ by __________ $$x$$-axis.
Q2.Match each piece of function notation to a description.
$$\text{f}(x)+1$$ - The output of $$\text{f}(x)$$ has $$1$$ added to it.
$$\text{f}(x+1)$$ - The input has $$1$$ added to it before the function is applied.
$$-\text{f}(x)$$ - The output of $$\text{f}(x)$$ is multiplied by $$-1$$
$$\text{f}(x)-1$$ - The output of $$\text{f}(x)$$ has $$1$$ subtracted from it.
$$\text{f}(x-1)$$ - The input has $$1$$ subtracted before the function is applied.
Q3.The transformation of shape 'a' to shape 'b' could be described by __________.
Q4.The transformation of the point $$(-3,2)$$ to the position $$(-3,-2)$$ could be described by __________.
Q5.The point $$(7,-9)$$ is reflected in the $$y$$-axis. What is its new position?
Q6.The point $$(-c,d)$$ is reflected in the $$y$$-axis. What is its new position?
Assessment exit quiz
6 Questions
Q1.$$\text{f}(-x)$$ is a transformation by __________.
Q2.$$\text{f}(-x)$$ is a transformation by reflection __________.
Q3.$$y=\text{f}(x)$$ is graphed. Which of these images shows the graph of $$y=\text{f}(-x)$$?
Q4.Which point will remain invariant by the transformation $$y=\text{f}(-x)$$? Give your answer in the form $$(x,y)$$
Q5.Here is a table of values for an unknown function $$\text{f}(x)$$. Which coordinate pairs will be on the graph $$y=\text{f}(-x)$$?
Q6.$$(e,f)$$ is on the graph of $$y=\text{f}(x)$$, $$e\neq{0}$$ and $$f\neq{0}$$. What will be the position of this point on the graph $$y=\text{f}(-x)$$?
