Writing Exponential Functions from Tables & Graphs

What does the base of an exponential function represent?

• It determines the maximum value of the function.

• It indicates the growth (if > 1) or decay (if < 1) rate of the function.

• It represents the x-intercept of the function.

• It defines the domain of the function.

What is the significance of the y-intercept in an exponential function?

• It represents the value of the function when @@x = 0@@, which is the initial amount before any growth or decay occurs.

• It indicates the rate of growth of the function at any point.

• It shows the maximum value the function can reach.

• It represents the horizontal asymptote of the function.

What is the formula for exponential decay?

• f(x) = a \times (1 - r)^x

• f(x) = a \times (1 + r)^x

• f(x) = a \times e^{-rt}

• f(x) = a \times r^x

What is a common mistake when identifying exponential functions?

• Confusing exponential functions with linear functions, which have a constant difference rather than a constant ratio.

• Believing that all exponential functions increase without bound.

• Assuming that exponential functions can only be positive.

• Thinking that exponential functions are always represented by a straight line.

What role does the constant 'a' play in an exponential function?

• It represents the rate of growth or decay of the function.

• It indicates the direction of the graph (upward or downward).

• It represents the initial value or starting amount of the function before any growth or decay occurs.

• It determines the period of oscillation in the function.

How can you verify if a function is exponential?

• By checking if the ratio of consecutive outputs is constant.

• By ensuring the function is defined for all real numbers.

• By determining if the function has a maximum or minimum value.

• By checking if the function is a polynomial of degree two.

What is the general form of an exponential function?

• f(x) = a \times b^x

• f(x) = a + b^x

• f(x) = a - b^x

• f(x) = a / b^x

What is the difference between growth and decay in exponential functions?

• Growth occurs when the base @@b > 1@@, while decay occurs when the base @@0 < b < 1@@.

• Growth occurs when the base @@b < 1@@, while decay occurs when the base @@b > 1@@.

• Growth and decay are both represented by the same base value.

• Growth occurs when the function is increasing, while decay occurs when the function is decreasing.

How can you determine the initial value of an exponential function from a graph?

• By finding the x-intercept of the graph

• By determining the slope of the graph

• By identifying the y-intercept of the graph, which is the value of @@f(0)@@

• By calculating the area under the curve

How do you find the equation of an exponential function from a set of points?

• By using the points to determine the initial value and the base by solving the equations formed by the points.

• By averaging the y-values of the points and using the average as the base.

• By plotting the points on a graph and drawing a line through them.

• By finding the midpoint of the x-values and using it as the initial value.