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Horizontal stretching and compression: Affects the width of the graph by looking at the value of k

Vertical stretching and compression: Affects the height of the graph by looking at the value of a

Y-axis reflection: Reflection in the Y-axis.

X-axis reflection: Reflection in the X-axis.

Horizontal Translation: Moves the graph to the left or right.

Vertical Translation: Moves the graph up or down.

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Exponential growth: A function whose variable is exponential and whose base is greater than 1. They have shown quick growth over time.

Exponential decay: A function in which the variable is in an exponent and the base is between 0 and 1. Over time, they decay quickly.

Domain and range: The domain of an exponential function is real, and the range depends on whether it grows or decays.

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An integer exponent represents an integer power of a number.

When the exponent is positive, it represents repeated multiplication of the base.

When the exponent is a negative, it means that the reciprocal of the base number is a positive exponent.

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The law of exponents is the behavior of exponents in multiplication, division, and exponentation operations.

The key laws include the product of powers, power of a power, power of a product, and quotient of powers.

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f(x)-final number

a-initial number

b-exponential growth or decay

1. if there is growth，b=1+growth rate

2. if there is decay，b=1-decay rate

x-number of growth or decay periods

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Make sure the units are consistent

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Rational exponents are exponents expressed as fractions.

They represent roots or fractional powers of a number.