Last updated on Oct 24, 2026

Using Log Graphs in Modelling (AQA A-Level Mathematics): Flashcards

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Using Log Graphs in Modelling

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Asymptote of $y = \log_a(x)$ where $a > 1$

$x = 0$

Asymptote of exponential graphs $y = a^x$

$y = 0$

Behaviour of $y = \log_a(x)$ curve as $x$ increases

Starts steep, becomes less steep, never horizontal

Translation for $y = \ln(x + 3)$

3 units to the left

Asymptote of $y = \ln(x + 3)$

$x = -3$

Transform $y = e^x$ to $y = 2e^x$

Stretch by factor 2, parallel to $y$ -axis

Transform $y = 2e^x$ to $y = 2e^{3x}$

Stretch by factor $\frac{1}{3}$ , parallel to $x$ -axis

Asymptote of $y = 2e^{3x}$

$y = 0$

Y-intercept of $y = 2 \times 3^x$

$(0, 2)$

Does $y = 2 \times 3^x$ intersect $x$ -axis?

No, approaches zero asymptotically

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