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 x axis
Keywords
Transformation - A transformation is a process that may change the size, orientation or position of a shape or graph.
Common misconception
Pupils can get confused between $$-$$f$$(x)$$ and f$$(-x)$$, which one is a reflection in the $$x$$-axis and which is a reflection in the $$y$$-axis?
Interpreting the notation is key. Remind pupils that $$-$$f$$(x)$$ is the output of f$$(x)$$ being multiplied by $$-1$$. Which coordinate is the output? The $$y$$ coordinates are altered from positive to negative, that is a reflection in which axis?
Licence
Lesson video
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Prior knowledge starter quiz
6 Questions
Q1.$$\text{f}(x)+a$$ and $$\text{f}(x+a)$$ transform the graph of $$\text{f}(x)$$ by __________.
Q2.Match each piece of function notation to a description.
$$\text{f}(x)+5$$ - The output of $$\text{f}(x)$$ has $$5$$ added to it.
$$\text{f}(x+5)$$ - The input has $$5$$ added to it before the function is applied.
$$5\text{f}(x)$$ - The output of $$\text{f}(x)$$ is multiplied by $$5$$
$$\text{f}(x)-5$$ - The output of $$\text{f}(x)$$ has $$5$$ subtracted from it.
$$\text{f}(x-5)$$ - The input has $$5$$ subtracted before the function is applied.
Q3.The transformation of the point $$(3,4)$$ to the position $$(-3,4)$$ could be described by __________.
Q4.The transformation of the point $$(-2,5)$$ to the position $$(-2,-5)$$ could be described by __________.
Q5.The point $$(7,-9)$$ is reflected in the $$x$$-axis. What is its new position?
Q6.The point $$(-a,b)$$ is reflected in the $$x$$-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 here. Which coordinate pairs will be on the transformed graph $$y=-\text{f}(x)$$?
Q4.$$y=\text{f}(x)$$ is graphed. Which of these images shows the transformation $$y=-\text{f}(x)$$?
Q5.Here is a table of values for an unknown function $$\text{f}(x)$$ Which coordinate pairs will be on the transformed graph $$y=-\text{f}(x)$$?
Q6.$$(-c,-d)$$ is on the graph of $$y=\text{f}(x)$$, $$c\neq{0}$$ and $$d\neq{0}$$. What will be the position of this point on the graph $$y=-\text{f}(x)$$?
