Graphing Logarithmic Functions (VCE SSCE Mathematical Methods): Quizzes

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Graphing Logarithmic Functions
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How are logarithmic and exponential function graphs related?

Reflections across y=xy = x

Which point is ALWAYS the x-intercept of y=logaxy = \log_a x?

(1,0)(1, 0)

What is the domain of the basic function y=logaxy = \log_a x?

R+\mathbb{R}^+ (positive reals)

For y=loga(mxn)y = \log_a(mx - n) where m>0m > 0, where is the vertical asymptote?

x=nmx = \frac{n}{m}

When base a>1a > 1, what property does y=logaxy = \log_a x have?

Strictly increasing

What is the domain of y=loga(mxn)y = \log_a(mx - n) where m>0m > 0?

(nm,)(\frac{n}{m}, \infty)

For y=loga(mxn)y = \log_a(mx - n) where m>0m > 0, what is the x-intercept?

x=1+nmx = 1 + \frac{n}{m}

What transformation does the negative in y=log3(x+4)y = -\log_3(x + 4) represent?

Reflection in x-axis

What is the base conversion formula for logax\log_a x in terms of base bb?

logbxlogba\frac{\log_b x}{\log_b a}

What is the range of the basic function y=logaxy = \log_a x?

R\mathbb{R} (all reals)

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