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

The basic family has base \(\frac{625}{256}\). The two marked exact points used in the feature table are P=\((-1,\frac{256}{625})\) and Q=\((0,1)\)

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 y>0, and the asymptote is y=1

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=0

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

(b)1 mark

State whether the graph increases or decreases as x increases

The graph decreases as x increases

The graph increases as x increases

Complete the exact feature table

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