Question

A) graph the function: f(x) = -2^xB) domain of the function?C) range of the function?D) Equation of the asymptote?E) y-intercept of the graph?

Answer 1

We are given the following function:

`y=-2^x`

Part A. We are asked to draw the graph of the function. This is an exponential function with a negative sign, this means that the graph is reflected across the x-axis. Therefore, the graph is:

Part B. The domain of a function is the values that the fuction can take as an input. Since the function is an exponential function, it can take any value of "x" therefore, the domain is all the real numbers, we write this as follows:

`D=(-\infty,\infty)`

Part B. The range of a function is the values that the function outputs, The range of an exponential function are the values that are greater than zero, but since the given function is reflected across the x-axis, this means that the rage is the negative real numbers, therefore, the range is:

`R=(-\infty,0)`

Part D. For an exponential function of the form:

`y=a(b^x)`

The asymptote is x-axis, since zero is never an output of the function. Therefore the equation of the asymptote is:

`y=0`

Part E. The y-intercept is the value of the function when "x = 0", therefore, substituting in the function we get:

`f(0)=-2^0`

Solving the operations:

`f(0)=-1`

Therefore, the y-intercept is -1