Since it fails the vertical line test - i.e. there is a section in which a vertical line passes through more than one point on the curve - it must be a relation.

Linear functions - which are straight lines on a co-ordinate grid - have an \(x\) term with a maximum power of \(1\), which we of course do not write in mathematics. \(w(x)\) is a quadratics function, \(q(x)\) is a rational function and \(v(x)\) is an exponential function.

If you substitute \(x=2\) into the functin you obtain 0.133.

If no toys are sold, \(t=0\), and hence \(N(0)=-100\) dollars.

Start by substituting \(14\) into the equation: \(14=\frac{3+x}{x^2}\)

Using your GDC, graph each side of the equation and find the point of interestion of these graphs.

Since we are only interested in the \(x\space co-ordinate\) of that intersection point, you find \(x=0.25\)

If \(f\) takes an input of \(10\) and produces an output of \(25\), then the inverse of \(f\), \(f^{-1}\), does the opposite.

If you input the graph of \(f(x)=\sqrt{x}\) into your GDC, you will notice that it does not exist for any negative value of \(x \), because we cannot take the square root of a negative number and obtain a real answer. The domain is therefore, \(x \geq 0\).

If you completed the previous question, then you will already be aware the the domain of a function, is the same the range of its inverse. Therefore, the range of \(f(x)=x^2 \) is \(f(x) \geq0\). This can also been seen through inputting the graoh into your GDC, or noting that when you square any input number, the output will always be positive or zero.

The domain and range of diagonal straight lines is all real numbers. This is not the case for horizontal or vertical lines.

To obtain the inverse function graphically, reflect it in the diagonal line, y = x.