which statement about the graph of y = 12 (0.75)^x is true?
A the coordinates of the x-intercept are (0.75, 0)
B the coordinates of the y-intercept are (0,12)
C the equation of the asymptote is x = 0
D the graph includes the point (2,1)
The correct answer is B, the coordinates of the y-intercept are (0,12).
To find the y-intercept, we can set x to zero and solve for y:
y = 12 (0.75)^0
y = 12
Therefore, the y-intercept is (0,12).
Option A is incorrect because (0.75,0) does not lie on the graph since plugging in x = 1 results in y = 9, not 0.
Option C is incorrect because the graph does not have an asymptote since the function approaches 0 as x approaches infinity.
Option D is incorrect because (2,1) does not lie on the graph since plugging in x = 2 results in y = 6.75, not 1.