Concept explainers
Describe how to transform the graph of
In order to obtain the graph of h(x), translate the graph of function f(x) down by 2 units followed by vertically stretches by 3 units and finally reflected about the x-axis.
Given:
Calculation:
The given function is
The parent function is
We can see that 2 has been added to the function f(x). And as per the transformation rule, whenever we add any constant ‘c to the function, then the graph will translate up by c units.
Hence, the graph will be translated up by 2 units.
Moreover, 3 is multiplied as with x as well. Since, 3 is greater than 1. Hence, the graph stretches vertically by 3 units.
Finally, we have negative sign before the function. As per the rule when the graph is reflected out x -axis then
Therefore, the graph is reflected out x-axis,
Therefore, in order to obtain the graph of h(x), translate the graph of function f(x) down by 2 units followed by vertically stretches by 3 units and finally reflected about the x-axis.
Below, is the graph.
Chapter 2 Solutions
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