1 of 8 0-day streak

Analyse exponential and logarithmic graphs

Question 1 of 8

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The function below is to be described using exact coordinates and transformations

f(x)=\frac{256}{625}^{\left(x\right)}

The basic family has base \(\frac{256}{625}\). The two marked exact points used in the feature table are P=\((1,\frac{256}{625})\) and Q=\((2,\frac{65536}{390625})\)

Their basic-family exponent values are \(t=1\) for P and \(t=2\) for Q

(a)1 mark

Select the statement that gives the domain, range and asymptote

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

The domain is all real numbers, the range is \(y>0\), and the asymptote is \(y=1\)

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

The domain is all real numbers, the range is \(y>0\), 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 P y-coordinate of the y-intercept horizontal asymptote coordinate y-coordinate of Q x-coordinate of Q y-coordinate of P