Question

Which graph has the following properties?

The y-intercept is at (0,6)
.
The horizontal asymptote is at y=1
.
The graph is decreasing for all values of x.
(1 point)
Responses

A coordinate plane's axes range from negative 1 to 8, both by 1-unit increments. A solid curve and a dotted line with arrows at both ends are plotted. The solid curve passes through a point plotted on the y-axis.
▼Click for Long Desc
The coordinates of the plotted point are left parenthesis 0 comma 6 right parenthesis. The solid curve is labeled y equals 6 multiplied by left parenthesis 0.45 right parenthesis superscript x baseline. The dotted line is plotted on the x-axis and horizontally extends from left parenthesis negative 1 comma 0 right parenthesis to left parenthesis 8 comma 0 right parenthesis. The solid curve decreases from the marked point to eventually overlap with the dotted line.

Image with description A coordinate plane's axes range from negative 1 to 8, both by 1-unit increments. A solid curve and a dotted line with arrows at both ends are plotted. The solid curve passes through a point plotted on the y-axis.

A coordinate plane's axes range from negative 1 to 8, both by 1-unit increments. A solid curve and a dotted line with arrows at both ends are plotted. The solid curve passes through a point plotted on the y-axis.
▼Click for Long Desc
The coordinates of the plotted point are left parenthesis 0 comma 6 right parenthesis. The solid curve is labeled y equals 5 multiplied by left parenthesis 0.45 right parenthesis superscript x baseline plus 1. The dotted line is plotted at y equals 1. The solid curve decreases from the marked point to eventually overlap with the dotted line.

Image with description A coordinate plane's axes range from negative 1 to 8, both by 1-unit increments. A solid curve and a dotted line with arrows at both ends are plotted. The solid curve passes through a point plotted on the y-axis.

A coordinate plane's x-axis ranges from negative 1 to 6 and its y-axis ranges from negative 1 to 8, both by 1-unit increments. A solid curve and a dotted line with arrows at both ends are plotted. The solid curve passes through plotted point.
▼Click for Long Desc
The plotted point is located on the y-axis at left parenthesis 0 comma 7 right parenthesis. The solid curve is labeled y equals 6 multiplied by left parenthesis 0.45 right parenthesis superscript x baseline plus 1. The dotted line is plotted at y equals 1. The solid curve decreases from the marked point to eventually overlap with the dotted line.

Image with description A coordinate plane's x-axis ranges from negative 1 to 6 and its y-axis ranges from negative 1 to 8, both by 1-unit increments. A solid curve and a dotted line with arrows at both ends are plotted. The solid curve passes through plotted point.

A coordinate plane's x-axis ranges from negative 1 to 8 and its y-axis ranges from negative 1 to 8, both by 1-unit increments. A solid curve and a dotted line with arrows at both ends are plotted. The solid curve passes through a plotted point.
▼Click for Long Desc
The coordinates of the marked point are left parenthesis 0 comma 6 right parenthesis. The solid curve is labeled y equals 6 multiplied by left parenthesis 0.45 right parenthesis superscript x baseline. The dotted line is plotted at y equals 0. The solid curve decreases from the plotted point, quickly flattens out, then continues just above the dotted horizontal line. The curve gets closer to the horizontal dotted line but never touches it.

Image with description A coordinate plane's x-axis ranges from negative 1 to 8 and its y-axis ranges from negative 1 to 8, both by 1-unit increments. A solid curve and a dotted line with arrows at both ends are plotted. The solid curve passes through a plotted point.
Remaining Attempts : 3

Answer 1

The graph labeled y = 5(0.45)^x + 1 (the one with the solid curve through (0,6) and the horizontal dotted line y = 1).

Reason: y(0) = 5 + 1 = 6, horizontal asymptote y = 1, and 0 < 0.45 < 1 makes the graph decreasing.