Question

use the b and d - sliders to find the exponential function in the form f(x)=b^x + d that has a horizontal asymptote at y = - 4 and passes through the point (1,0). what integer values of b and d make a function that meets these criteria?
use the interactive figure to find your answer. use the left and right arrow keys to move along a slider as needed.
click here to launch the interactive figure.

b =

d =

Explanation:

Step1: Recall the horizontal asymptote property

For an exponential function \(y = b^{x}+d\), the horizontal asymptote is \(y = d\). Given the horizontal asymptote \(y=-4\), so \(d=-4\).

Step2: Substitute the point \((1,0)\) into the function

Substitute \(x = 1\), \(y = 0\) and \(d=-4\) into \(y=b^{x}+d\). We get \(0=b^{1}-4\).

Step3: Solve for \(b\)

From \(0 = b - 4\), we can add \(4\) to both sides of the equation. So \(b=4\).

Answer:

\(b = 4\), \(d=-4\)