Exponential Function Transformations

Front

What is an exponential function?

Back

An exponential function is a mathematical function of the form f(x) = a * b^x, where 'a' is a constant, 'b' is a positive real number, and 'x' is the exponent.

Front

What is the horizontal asymptote of an exponential function?

Back

The horizontal asymptote of an exponential function f(x) = a * b^x + k is the line y = k, which the graph approaches as x approaches positive or negative infinity.

Front

What is the domain of an exponential function?

Back

The domain of an exponential function is all real numbers, represented as (-∞, ∞).

Front

What is the range of an exponential function?

Back

The range of an exponential function f(x) = a * b^x is (0, ∞) if a > 0, and (-∞, 0) if a < 0.

Front

What is a parent function in the context of exponential functions?

Back

The parent function of exponential functions is f(x) = b^x, where b > 0.

Front

How does a vertical shift affect the graph of an exponential function?

Back

A vertical shift of k units in the function f(x) = a * b^x + k moves the graph up if k > 0 and down if k < 0.

Front

How does a horizontal shift affect the graph of an exponential function?

Back

A horizontal shift of h units in the function f(x) = a * b^(x - h) moves the graph to the right if h > 0 and to the left if h < 0.

Front

What does it mean to stretch or compress an exponential function?

Back

Stretching an exponential function means increasing the value of 'a' (the coefficient), making the graph steeper, while compressing means decreasing 'a', making the graph flatter.

Front

What is the effect of a negative coefficient in an exponential function?

Back

A negative coefficient in an exponential function f(x) = -a * b^x reflects the graph across the x-axis.

Front

What transformation occurs in the function f(x) = 2^(x+1) - 3?

Back

This function is translated left 1 unit and down 3 units from the parent function f(x) = 2^x.