can someone help me please :(

Question

Graph y=3(2)*      

a. number of x intercept

b. what is the y intercept

c. domain and range

d. end behavior

Answer 1

The exponential function y = 3(2)^x

General form of exponential function y = ab^x where b > 0.

Where the parameter a is called function's  y intercept and the parameter b is called base of the function.

y = 3(2)^x

Compare it to y = ab^x

a = 3, b = 2

Make the table of values to find ordered pairs that satisfy the equation.

Choose random values for x and find the corresponding values for y.

x	y = 3(2)x	(x, y)
- 4	y = 3(2)-4	(-4, 0.1875)
-3	y = 3(2)-3	(-3, 0.375)
-2	y = 3(2)-2	(-2, 0.75)
-1	y = 3(2)-1	(-1, 1.5)
0	y = 3(2)0	(0, 3)
1	y = 3(2)1	(1, 6)

Graph

Draw the coordinate plane.

Plot the points found in the table.

Connect the plotted points smooth curve.

a) Exponential function does not have any x intercepts.

There is no x intercepts for the function y = 3(2)^x.

Answer 2

b)

y = 3(2)^x

Compare it to exponential function y = ab^x

Since a = 3, y intercept of the function is 3.

Answer 3

c) y = 3(2)^x

Domain of the exponential function is all real numbers.

Domain in interval notation (- ∞, ∞)

Range of the function

It's range is all positive real numbers .

Range in interval notation (0, ∞).

Answer 4

d) The function y = 3(2)^x

Compare it to exponential function y = ab^x

a = 3, b = 2

End behavior

Since b > 1, the function is increasing.

As x value approach positive infinity(x → ∞), y value approach positive infinity(y → ∞).

As x value approach negative infinity(x → - ∞), y value approach zero(y → 0).