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Compared to the graph of the base function , the graph of the function is translated

What is the equation of the transformed function, g(x), after the transformations are applied to the graph of the base function , shown in blue, to obtain the graph of g(x), shown in red?

When a function is reflected in the x-axis, the coordinates of point (x, y) become

The function represents a transformation that can best be described as

When the value of a is less than –1, the function has what relationship to the base function ?

For each g(x), describe the transformation(s) from the base function .
a)
b)
c)

The approximate height, h, in metres, of an object above the ground after it is dropped from a distance, d, in metres, can be modelled by the function , where t is the time, in seconds, after being dropped.
a) Determine the function for an object being dropped from each height.
i) 400 m
ii) 550 m
iii) 850 m
b) Graph all three functions on the same set of axes.
c) Describe the transformation that relates the highest curve to the lowest curve.
d) Describe the transformation that relates the highest curve to the curve in the middle.

For the base function , a reflection in the y-axis is followed by a reflection in the x-axis.
a) Discuss the effect of each reflection on the base function.
b) Is there a point that you expect to be invariant during these reflections? If so, state its coordinates.
c) Graph the function after each reflection.
d) Use your graph in part c) to verify your answer for part b).
e) Make a general statement regarding invariant points after reflections in the x-axis and the y-axis.