Complete the questions to practice determining if an equation represents an exponential function.

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  1. Determine whether each equation represents an exponential function. Explain your reasoning.
    a.

    \(y=3x^2\)
    b.

    \(y=\frac{1}{3}\left(2\right)^x\)
    c.

    \(y=0.5\left(-3\right)^x\)
    d.

    \(y=-4\left(\frac{1}{2}\right)^x\)

In the following Check it Out activity, you will explore the equation y = abx, an exponential function. You will be asked to describe its end behaviour and identify the y-intercept. In Highlights, you will review these two terms briefly before continuing.
  • Read the following carefully, and talk to your teacher if you have any questions.

End behaviour is what happens to the y-value of a function as x approaches positive or negative infinity. When describing the end behaviour of a function, you must state if the graph is increasing or decreasing at both the left and right extremes of the coordinate plane. Often, stating the quadrants through which a function moves is considered part of the description of end behaviour.

At some point, every function crosses the y-axis. The y-value of this point is the y-intercept. A function can have only one y-intercept.