Questions: 10/(1/4)

Solution Steps

The graph resembles the graph of a tangent function.

The graph has vertical asymptotes at $x=-4$ and $x=1$. The midpoint between these asymptotes is $x=-\frac{3}{2}$. This suggests a horizontal shift of $\frac{3}{2}$ units to the left.

The graph appears to pass through the point $(-\frac{3}{2}, -3)$, which suggests a vertical shift of 3 units down.

Normally, the tangent function takes on a value of 1 when evaluated at a point halfway between the vertical asymptotes. In this case, when $x = -1$ (halfway between -4 and 1), $y = -2$. So the graph increases by 1 unit when $x$ increases by 3 units. Since a normal tangent graph would increase by 1 unit when x increases by $\frac{\pi}{4}$ units, this graph has been horizontally scaled by a factor of $\frac{3}{\pi / 4} = \frac{12}{\pi}$. The period of this graph is $1-(-4) = 5$. The usual period of tangent is $\pi$, so there's a horizontal stretch of $\frac{5}{\pi}$. Therefore, we must scale the input by $\pi/5$.

Final Answer: