Exponential and Logarithmic Functions — Test

Question 4 • Algebra 2 with Probability

Which of the following shows the graph of y is equal to 4 to the x th power plus 3 ?

Answer

Image with description On a coordinate plane, the x and y axes ranging from negative 10 to 10 in increments of 1 with major tick marks at even integers. A curve has a horizontal asymptote at y equals 0 as x approaches negative infinity, indicated by an arrow pointing left along the x-axis. It passes through the points (3 comma 1) and (4 comma 4). As x increases, the curve rises sharply towards positive infinity, indicated by an arrow pointing up and right.

Image with description On a coordinate plane, the x and y axes ranging from negative 10 to 10 in increments of 1 with major tick marks at even integers. A curve has a horizontal asymptote at y equals 0 as x approaches negative infinity, indicated by an arrow pointing left along the x-axis. The curve passes through the points (negative 3 comma 1), (negative 2 comma 4), and (negative 1 point 5 comma, 8). As x increases, the curve rises sharply towards positive infinity, indicated by an arrow pointing up and right.

Image with description On a coordinate plane, the x and y axes ranging from negative 10 to 10 in increments of 1 with major tick marks at even integers. A curve has a horizontal asymptote at y equals 3 as x approaches negative infinity. It passes through the points (negative 2 comma 3), (0 comma 4) and (1 comma 7). As x increases, the curve rises sharply towards positive infinity. As x decreases, the curve flattens out, approaching the asymptote at y equals 3.

Image with description On a coordinate plane, the x and y axes ranging from negative 10 to 10 in increments of 1 with major tick marks at even integers. A curve has a horizontal asymptote at y equals negative 3 as x approaches negative infinity, indicated by an arrow pointing left along the line y equals negative 3. It passes through the y-intercept (0 comma negative 2). The curve goes through the points (negative 1 comma negative 3), (1 comma 1) and (1 point 5 comma 6). As x increases, the curve rises sharply towards positive infinity, indicated by an arrow pointing up and right.

Explanation

For y = 4^x + 3, the graph of 4^x is shifted up 3 units, so its horizontal asymptote is y = 3. At x = 0, y = 4^0 + 3 = 4, and at x = 1, y = 4 + 3 = 7. Choice C has the asymptote y = 3 and passes through (0, 4) and (1, 7).

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