Chapter 6

Study graphs of the functions \(y=x^{2}\) and \(y=-x^{2}\). Are these continuous functions?

Explain why a many-to-one function does not have an inverse function. Give an example.

Given the function \(g(t)=8 t+3\) find (a) \(g(7)\) (b) \(g(2)\) (c) \(g(-0.5)\) (d) \(g(-0.11)\)

Consider the parametric equations \(x=+\sqrt{t}, y=t\), for \(0 \leq t \leq 10\) (a) Draw up a table of values of \(t, x\) and \(y\) for values of \(t\) between 0 and 10 (b) Plot a graph of this function. (c) Obtain an explicit equation for \(y\) in terms of \(x\).

Illustrate why \(y=x^{4}\) is a many-to-one function by providing a suitable numerical example.

If \(f(x)=8 x+2\) find \(f(f(x))\).

When stating the coordinates of a point, which coordinate is given first?

Sketch a graph of a periodic function that has no discontinuities.

Explain the meaning of an expression such as \(y(x)\) in the context of functions. What is the interpretation of \(x(t) ?\)

By sketching a graph of \(y=3 x-1\) show that this is a one-to-one function.