Question

review for exam 3 over chapters 6 and 11
score: 10/26 answered: 13/26
question 9
graph the logarithmic function ( y=log _{4}(x) ) by plotting the horizontal intercept and one other point.
clear all draw:
question help: video
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Explanation:

Step1: Find the horizontal intercept

The horizontal intercept occurs when \(y = 0\).
Set \(y=\log_{4}(x)=0\).
Using the property \(\log_{a}(b)=c\) implies \(a^{c}=b\), so \(4^{0}=x\), then \(x = 1\). The point is \((1,0)\).

Step2: Find another point

Let \(x = 4\).
Substitute \(x = 4\) into \(y=\log_{4}(x)\), then \(y=\log_{4}(4)\).
Using the property \(\log_{a}(a)=1\), so \(y = 1\). The point is \((4,1)\).

Answer:

Plot the points \((1,0)\) and \((4,1)\) on the coordinate - plane and draw a curve passing through these points (since the domain of \(y=\log_{4}(x)\) is \(x>0\) and the function is increasing).