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NSWMaths AdvancedQuick questions
Year 11: Exponential and Logarithmic Functions
Quick questions on Exponential and logarithmic graphs for HSC Maths Advanced: the shape of y=a^x and y=log_a x, the horizontal asymptote of an exponential and the vertical asymptote of a logarithm, the reflection in y=x that makes them inverse functions, transformations by translation, reflection and dilation, and stating domain and range
4short Q&A pairs drawn directly from our worked dot-point answer. For full context and worked exam questions, read the parent dot-point page.
What is the shape of an exponential graph y = a^x?Show answer
For a base , the graph of has one characteristic shape: it rises from left to right, getting steeper and steeper, and it stays entirely above the -axis. Three features pin it down on any sketch, and all three come straight from the index laws:
What is the shape of a logarithmic graph y = log_a x?Show answer
The graph of (with ) is the exponential's twin. It rises from left to right but the other way round: it climbs steeply near the start and then flattens as grows. Its three features are the exponential's features with and swapped:
What is transforming an exponential graph?Show answer
Every transformation you met for parabolas and other curves works here unchanged. Start from a known exponential like or and apply the move; the key is to track the asymptote, the intercept and the domain/range as you go, because those are the marks.
What is transforming a logarithmic graph?Show answer
Logarithms transform by the same rules, but watch the vertical asymptote, which is what a horizontal shift moves. Starting from (asymptote ):
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