What are the domain and range of the function y=2(3^x)-1?

[aisha]

I was given the equation y=2(3^x)-1 and told to state the domain, range, x and y intercepts and asymptotes.

I graphed the eqn and got the x-intercept to =-0.63 and the y-intercept=1
the vertical asymptote is the same as x-intercept so =-0.63 and the horizontal asymptote always equals 0.

If these values are right, then I need to find out the domain and range, but I don't know how. Can someone please help me?

 

[dextercioby]

I was given the equation y=2(3^x)-1 and told to state the domain, range, x and y intercepts and asymptotes.
I graphed the eqn and got the x-intercept to =-0.63 and the y-intercept=1
the vertical asymptote is the same as x-intercept so =-0.63 and the horizontal asymptote always equals 0.
If these values are right, then I need to find out the domain and range, but I don't know how. Can someone please help me?

Me again,...This time i say to review calculations.
Hints:1)Do u agree with me that the domain in the entire real axis and the range the open interval (-1,+infinity)??
2)Use the correct definitions of veritical/horizontal asymptotes.
3) Solve the equations for the intersections correctly.

PS I assumed that your initial function was $y=2\cdot 3^{x} -1$.

 

[wais]

The domain of a function is the set of all possible input values, or x-values, for which the function is defined. In this case, the function y=2(3^x)-1 is defined for all real numbers, so the domain is all real numbers, or (-∞, ∞). This means that any x-value can be plugged into the function and it will produce a valid output.

The range of a function is the set of all possible output values, or y-values, that the function can produce. In this case, the function y=2(3^x)-1 can produce any real number as an output, so the range is also all real numbers, or (-∞, ∞). This means that the function can have a y-value of any number, positive or negative, depending on the input x-value.

As for the x and y-intercepts, your calculations are correct. The x-intercept is approximately -0.63 and the y-intercept is 1. These values represent the points where the function crosses the x and y-axes, respectively.

The vertical asymptote, as you mentioned, is also located at -0.63. This is the value where the function approaches infinity as x approaches -0.63 from either side. The horizontal asymptote, as you also correctly stated, is always at y=0. This means that as x increases or decreases without bound, the function will approach 0 as well.

I hope this helps clarify the concepts of domain, range, x and y-intercepts, and asymptotes for this function. Keep up the good work!