An art collector purchased a painting at an auction. The function shown represents the value of the painting in dollars, y, after x years.
y = 575(1.045)x
Which statements about the graph of the function are true?
Select TWO correct answers.
Option 1
The x-intercept of the graph is 575.
Option 2
The graph has an asymptote at x = 0.
Option 3
The y-intercept of the graph is 575.
Option 4
The graph decreases as the value of x increases.
Option 5
The graph has an asymptote at y = 0.
The correct options are:
Option 1: The x-intercept of the graph is 575.
This is true because an x-intercept is a point on the graph where y = 0. In this case, plugging in y = 0 into the equation gives 0 = 575(1.045)^x. The only way for this to be true is if x = 0.
Option 3: The y-intercept of the graph is 575.
This is true because a y-intercept is a point on the graph where x = 0. In this case, plugging in x = 0 into the equation gives y = 575(1.045)^0 = 575.
Option 2: The graph has an asymptote at x = 0.
This is false because there is no asymptote at x = 0. The graph is a exponential growth curve, meaning it will continue to increase without bound as x increases.
Options 4 and 5 are false because the graph of the function is an exponential growth curve, meaning it increases as x increases and does not have a horizontal asymptote at y = 0. Therefore, the correct answers are options 1 and 3.