Modelling with Exponentials & Logarithms (Edexcel A-Level Mathematics): Quizzes

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Using Log Graphs in Modelling
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What is the asymptote of the logarithmic graph y=log⁡a(x)y = \log_a(x) where a>1a > 1?

x=0x = 0

What is the asymptote of exponential graphs y=axy = a^x?

y=0y = 0

How does the logarithmic curve y=log⁡a(x)y = \log_a(x) behave as xx increases?

Steep start, becomes less steep

To sketch y=ln⁡(x+3)y = \ln(x + 3) from y=ln⁡(x)y = \ln(x), which translation is applied?

3 units to the left

What is the asymptote of the graph y=ln⁡(x+3)y = \ln(x + 3)?

x=−3x = -3

What is the first transformation to sketch y=2e3xy = 2e^{3x} from y=exy = e^x?

Stretch factor 2 parallel to yy-axis

At which point does y=2×3xy = 2 \times 3^x intersect the yy-axis?

(0,2)(0, 2)

Does the curve y=2×3xy = 2 \times 3^x intersect the xx-axis?

No, it approaches zero asymptotically

What is the asymptote of the graph y=2e3xy = 2e^{3x}?

y=0y = 0

What is the value of log⁡28\log_2{8} used in simplifying the intersection equation?

33

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