Exponential Functions - 1st Sem GenMath

kaˣ

State the formula for an exponential function:

Exponential growth

When a>1, the graph goes from left to right.

Exponential decay

When 0

Half-life

The time it takes for a radioactive substance to decay.

Compound interest

Sum of interest of prior periods computed on the original or principal amount and each of the successive periods on both principal and interest.

F=P(1+r/n)ᵗⁿ

State the formula for a compound interest:

1

If the annual interest is compounded annually, then n = _____.

2

If the annual interest is compounded semiannually, then n = _____.

4

If the annual interest is compounded quarterly, then n = _____.

1

Zero exponent; a⁰ = _____

1/aⁿ

Negative exponent; a⁻ⁿ = _____

aᵐ⁺ⁿ

aᵐ⋅aⁿ = _____

aᵐ⁻ⁿ

aᵐ/aⁿ = _____

aᵐⁿ

Power of a power; (aᵐ)ⁿ = _____

aⁿbⁿ

Power of a product; (ab)ⁿ = _____

aⁿ/bⁿ

Power of a quotient; (a/b)ⁿ = _____

One-to-one Property

If two expressions with the same bases are equal, then their exponents are equal.

None; (0,k); None; y=0/x-axis

f(x) = kaˣ

X-int: ______

Y-int: ______

V.A.: ______

H.A.: ______

kaˣ±c

State the formula for a vertical shift (upward or downward) in an exponential function:

Exists if k and c have opposite signs; (0,k+c); None; y=c

f(x) = kaˣ±c

X-int: ______

Y-int: ______

V.A.: ______

H.A.: ______

kaˣ±ᶜ

State the formula for a horizontal shift (right or left) in an exponential function:

Left

If f(x) = kaˣ⁺ᶜ, then f(x) is horizontally shifted to the _____.

Right

If f(x) = kaˣ⁻ᶜ, then f(x) is horizontally shifted to the _____.

Horizontal Line Test

If the horizontal line intersects the graph exactly once, then the graph is one-to-one.

y=x

Line of symmetry between a graph of a function and its inverse.