Question

exponential functions
you do/partner check

1. example f(x)= -1(2)^x

reflect? ____
y-intercept ____
equation of asymptote ____

Explanation:

Step1: Determine if there is a reflection

The general form of an exponential function is \(y = a(b)^{x}\). When \(a<0\), the graph is reflected over the \(x -\)axis. For \(y=-1(2)^{x}\), since \(a = - 1<0\), there is a reflection over the \(x -\)axis.

Step2: Find the \(y -\)intercept

To find the \(y -\)intercept, set \(x = 0\). Substitute \(x = 0\) into \(y=-1(2)^{x}\), we get \(y=-1(2)^{0}\). Since \(a^{0}=1\) (\(a
eq0\)), then \(y=-1\times1=-1\). So the \(y -\)intercept is \((0, - 1)\)

Step3: Find the equation of the asymptote

For an exponential function of the form \(y = a(b)^{x}+k\), the horizontal asymptote is \(y = k\). In the function \(y=-1(2)^{x}+0\), \(k = 0\). So the equation of the horizontal asymptote is \(y = 0\)

Answer:

Reflect? Yes (over the \(x -\)axis). Y - intercept: \((0,-1)\). Equation of Asymptote: \(y = 0\)