1 of 8 0-day streak

Analyse exponential and logarithmic graphs

Question 1 of 8

No calculator

Analyse the displayed graph rule and record its exact features

f(x)=\log_{\frac{4096}{6561}}\left(x\right)

The basic family has base \(\frac{4096}{6561}\). The two marked exact points used in the feature table are P=\((\frac{6561}{4096},-1)\) and Q=\((1,0)\)

Their basic-family exponent values are \(t=-1\) for P and \(t=0\) for Q

(a)1 mark

Select the statement that gives the domain, range and asymptote

The domain is all real numbers, the range is \(x>0\), and the asymptote is \(x=0\)

The domain is \(x>0\), the range is all real numbers, and the asymptote is \(x=0\)

The domain is \(x>0\), the range is all real numbers, and the asymptote is \(y=0\)

The domain is all real numbers, the range is all real numbers, and the asymptote is \(y=0\)

(b)1 mark

State whether the graph increases or decreases as x increases

The graph increases as x increases

The graph decreases as x increases

Complete the exact feature table

x-coordinate of the x-intercept x-coordinate of Q y-coordinate of Q x-coordinate of P vertical asymptote coordinate y-coordinate of P