Question Type 2: Drawing logarithmic functions as inverses of the exponential functions Bootcamps

Sketch $y=5^x$ and its inverse $y=\log_5(x)$, labelling the asymptotes, the line $y=x$, and the key points $(0,1)$ and $(1,5)$ with their reflections.

Sketch the graphs of $y = e^x$ and its inverse $y = \\ln(x)$ on the same axes. Label the asymptote, the line $y=x$, and the points corresponding to $(0,1)$ and $(1,e)$ with their reflections.

Sketch $y=e^{x-1}$ and its inverse $y=\ln(x)+1$. Label the asymptote, the line $y=x$, and the images of $(1,1)$ and $(2,e)$.

Sketch $y=\log_{1/2}(x)$ and its inverse $y=(1/2)^x$. Label asymptotes, line $y=x$, and the reflections of $(1,0)$ and $(2,-1)$.

Sketch $y=5^{2x}$ and its inverse $y=\tfrac12\log_5(x)$. Label asymptotes, the line $y=x$, and the images of $(0,1)$ and $(\tfrac12,5)$.

Sketch $y=3^{-x}$ and its inverse $y=-\log_3(x)$. Label asymptotes, line $y=x$, and images of $(0,1)$ and $(1,\tfrac13)$.

On one set of axes, sketch $y=2\ln(x)$ and its inverse $y=e^{x/2}$. Label asymptote, line $y=x$, and images of $(1,0)$ and $(e,2)$.

On one set of axes, sketch $y=2^x+3$ and its inverse $y=\log_2(x-3)$. Label the asymptote, line $y=x$, and key points.

Sketch $y=\frac{\ln(x)}{2\ln(5)}$ and its inverse $y=5^{2x}$. Label asymptotes, the line $y=x$, and the reflections of $(1,0)$ and $(5,\tfrac12)$.

Sketch $y=5^{x+2}-1$ and its inverse. State the equation of the inverse before sketching.

Sketch $y=\log_3(x-4)+2$ and its inverse. Determine the inverse explicitly before sketching.

Sketch $y=\tfrac13e^{x-1}$ and its inverse. Find the inverse equation before drawing.