Graphs of Exponential Functions (VCE SSCE Mathematical Methods): Flashcards

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Graphs of Exponential Functions
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Y-intercept of all y=axy = a^x graphs

(0,1)(0, 1)

Domain of y=axy = a^x

R\mathbb{R} (all real numbers)

Range of y=axy = a^x

R+\mathbb{R}^+ (positive real numbers)

Horizontal asymptote of y=axy = a^x

x-axis (line y=0y = 0)

Behaviour when a>1a > 1 in y=axy = a^x

Exponential growth (increasing)

Behaviour when 0<a<10 < a < 1 in y=axy = a^x

Exponential decay (decreasing)

Effect of larger bases when a>1a > 1

Steeper exponential growth

How y=(1a)xy = (\frac{1}{a})^x relates to y=axy = a^x

Reflection in the y-axis

Effect of vertical translation on asymptote

Shifts the asymptote

Sign of all y=axy = a^x output values

Always positive, never zero or negative

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