Exponential Functions — Domain, Range, and Graph Interpretation

A part of an exponential function is graphed on the grid. Which statements are true about the domain and range of the part of the function shown? Select TWO correct answers.

• The domain is the set of all real numbers greater than or equal to 1 and less than or equal to 8.

• The domain is the set of all real numbers greater than or equal to 2 and less than or equal to 5.

• The domain is the set of all real numbers.

• The range is the set of all real numbers greater than or equal to 1 and less than or equal to 8.

• The range is the set of all real numbers greater than or equal to 2 and less than or equal to 5.

Answer explanation

The correct domain is from 2 to 5, indicating the function is defined only in that interval. The range from 1 to 8 shows the output values of the function within that domain, confirming the selected statements are true.

A part of exponential function f is graphed on the grid. Which inequality best represents the domain of the part shown?

Answer explanation

The graph shows part of an exponential function, which typically has a domain of all real numbers. The correct inequality, x > -2, indicates that the part of the graph starts at x = -2 and extends to the right.

A part of an exponential function is graphed on the grid. Which inequality best represents the domain of the part shown?

Answer explanation

The graph of the exponential function starts at x = -2 and extends to the right. Therefore, the domain is best represented by the inequality x ≥ -2, indicating all x-values from -2 onwards.

What appears to be the domain of the part of the exponential function graphed on the grid?

Answer explanation

The domain of the graphed part of the exponential function is represented by the x-values. The correct choice, -1 ≤ x ≤ 3, indicates the range of x-values shown on the grid.

The graph of an exponential function is shown on the grid. Which statement is best represented by the graph of the function?

• The equation of the asymptote of the graph is x = 4.

• The function is increasing on the interval x > 0 and decreasing on the interval x < 0.

• The x-intercept of the graph of the function is (8, 0).

• The y-intercept of the graph of the function is (0, 3).

Answer explanation

The graph shows that the function crosses the y-axis at (0, 3), confirming the y-intercept is (0, 3). The other statements about the asymptote, intervals, and x-intercept are incorrect.

• Linear

• Quadratic

• Exponential

Answer explanation

The function f(x)=6(1/3)^x is an exponential function because it has the form a(b^x), where a is a constant and b is a base raised to the power of x. Thus, the correct choice is Exponential.

Answer explanation

The function f(x)=6(1/3)^x approaches 0 as x increases, indicating that the horizontal asymptote is y=0. This means the graph will get closer to the line y=0 but never actually touch it.

Answer explanation

To find points on the graph of f(x)=6(1/3)^x, calculate f(0) = 6 and f(1) = 6(1/3) = 2. Thus, (0,6) and (1,2) are correct points on the graph.

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Answer explanation

The equation y=5(1/3)^x represents an exponential decay function. Graph D shows a decreasing curve starting from 5, which matches the behavior of this function as x increases, making it the correct choice.

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Answer explanation

The function f(x)=2(5)^x is an exponential growth function. Graph F shows a rapid increase as x increases, which aligns with the behavior of this function. The other graphs do not represent this growth accurately.