6.4 Graphs of logarithmic functions  (Page 6/8)

Before graphing $f(x)=\log (-x),$ identify the behavior and key points for the graph.

• Since $b=10$ is greater than one, we know that the parent function is increasing. Since the input value is multiplied by $\mathrm{-1},$ $f$ is a reflection of the parent graph about the y- axis. Thus, $f(x)=\log (-x)$ will be decreasing as $x$ moves from negative infinity to zero, and the right tail of the graph will approach the vertical asymptote $x=0.$
• The x -intercept is $\left(\mathrm{-1},0\right).$
• We draw and label the asymptote, plot and label the points, and draw a smooth curve through the points.

The domain is $\left(-\infty ,0\right),$ the range is $\left(-\infty ,\infty \right),$ and the vertical asymptote is $x=0.$

Press [Y=] and enter $4\ln \left(x\right)+1$ next to Y ₁ =. Then enter $-2\ln \left(x-1\right)$ next to Y ₂ = . For a window, use the values 0 to 5 for $x$ and –10 to 10 for $y.$ Press [GRAPH] . The graphs should intersect somewhere a little to right of $x=1.$

For a better approximation, press [2ND] then [CALC] . Select [5: intersect] and press [ENTER] three times. The x -coordinate of the point of intersection is displayed as 1.3385297. (Your answer may be different if you use a different window or use a different value for Guess? ) So, to the nearest thousandth, $x\approx \mathrm{1.339.}$