Question

Use the graph of the exponential function to answer the following question.Which statements about the graph are TRUE? Select all that apply. A. The x-intercept is 2. B. The y-intercept is 3. C. The asymptote is y = -1D. The range is all real numbers E. The domain is all real numbers F. The function shows growth G. As x increases, y approaches, but never reaches, -1

Answer 1

The curve intersect the x axis at x = 1. So x-intercept is 1. Statement A is false.

The curve intersect the y-axis at y= 3. So y intercept is 3. Statement B is correct.

The curve tends toward infinity at y = -1. So y = -1 asysmptote of the function. Statement C is correct.

The range of function is y > -1. So range is not all real number. Thus statement D is incorrect.

The function is defined for x > -0.5. At x = 0.5 function tends toward infinity. Thus statement E is incorrect.

As we move from left to right on x-axis then function decreases. So function shows decay. The statement F is incorrect.

The value of function approaches -1 as value of x increase but does not cross -1 ot touch the value y = -1. So statement G is correct.

Thus correct statement are,

B, C and G.