Exponential Functions (Grade 10 NSC Matric Mathematics): Flashcards

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Exponential Functions
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Definition of exponential function

Function where variable appears as exponent

Basic form of exponential function

y=bxy = b^x where b>0b > 0 and b≠1b \neq 1

General form of exponential function

y=abx+qy = ab^x + q

Condition for exponential growth

When b>1b > 1

Condition for exponential decay

When 0<b<10 < b < 1

Domain of y=abx+qy = ab^x + q

All real numbers: {x:x∈R}\{x : x \in \mathbb{R}\}

Y-intercept of y=abx+qy = ab^x + q

(0,a+q)(0, a + q)

Horizontal asymptote of y=abx+qy = ab^x + q

y=qy = q

Range of y=abx+qy = ab^x + q when a>0a > 0

{f(x):f(x)>q}\{f(x) : f(x) > q\}

Range of y=abx+qy = ab^x + q when a<0a < 0

{f(x):f(x)<q}\{f(x) : f(x) < q\}

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