AP Precalculus Midterm Review

As x values increase without bound, what do the y-values approach in the function @@y=2ullet3^{-x}@@?

• y approaches 0

• y approaches 2

• y approaches infinity

• y approaches -2

What is the definition of a function composition?

• A function composition is the application of one function to the results of another, denoted as @@f(g(x))@@.

• A function composition is the process of adding two functions together.

• A function composition is the multiplication of two functions to create a new function.

• A function composition is the evaluation of a function at a specific point.

If @@f(x)=2x@@ and @@g(x)=2x^2-1@@, find @@f(g(x))@@.

• @@f(g(x)) = f(2x^2 - 1) = 2(2x^2 - 1) = 4x^2 - 2@@

• @@f(g(x)) = f(2x^2 - 1) = 2(2x^2 - 1) = 2x^2 - 1@@

• @@f(g(x)) = f(2x^2 - 1) = 2(2x^2 - 1) = 8x^2 - 2@@

• @@f(g(x)) = f(2x^2 - 1) = 2(2x^2 - 1) = 4x^2 + 2@@

What is the solution for @@log_2x^2 - log_24 = 3@@?

• x = 4 and x = -4

• x = 2 and x = -2

• x = 8 and x = -8

• x = 0 and x = 1

What is the definition of a vertical translation in graph transformations?

• A vertical translation shifts the graph up or down without changing its shape.

• A vertical translation rotates the graph around a point.

• A vertical translation reflects the graph across the x-axis.

• A vertical translation stretches the graph horizontally.

What is the definition of average rate of change?

• The average rate of change of a function over an interval is given by @@\frac{f(b) - f(a)}{b - a}@@.

• The average rate of change is the slope of the tangent line at a point on the graph.

• The average rate of change is the difference between the maximum and minimum values of a function.

• The average rate of change is the integral of a function over an interval.

What is the relationship between logarithmic and exponential functions?

• Logarithmic functions are the inverses of exponential functions.

• Logarithmic functions are a type of exponential function.

• Logarithmic functions and exponential functions are unrelated.

• Logarithmic functions are always greater than exponential functions.

What is the exponential decay function?

• An exponential decay function is of the form @@y = a ullet b^{-x}@@ where @@0 < b < 1@@.

• An exponential decay function is of the form @@y = a ullet b^{x}@@ where @@b > 1@@.

• An exponential decay function is of the form @@y = a + b^{x}@@ where @@b < 0@@.

• An exponential decay function is of the form @@y = a ullet e^{x}@@ where @@a > 0@@.

What is the logarithmic identity for subtraction?

• @@ ext{log}_a b - ext{log}_a c = ext{log}_a rac{b}{c}@@

• @@ ext{log}_a b + ext{log}_a c = ext{log}_a (b imes c)@@

• @@ ext{log}_a b - ext{log}_a c = ext{log}_a (b + c)@@

• @@ ext{log}_a b imes ext{log}_a c = ext{log}_a (b^c)@@