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please help me :(

0 votes
Graph y=6(1/2)*

- number of x intercepts

-what is the y intercepts

- domain and range

-end behavior
asked Nov 25, 2014 in CALCULUS by anonymous

4 Answers

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The exponential function y = 6(1/2)x

General form of exponential function y = abx where b > 0.

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

y = 6(0.5)x

Compare it to y = abx

a = 6, b = 0.5

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

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

x

y = 6(0.5)x

(x, y)

- 1

y = 6(0.5)-1

(-1, 12)

0

y = 6(0.5)0

(0, 6)

1

y = 6(0.5)1

(1, 3)

2

y = 6(0.5)2

(2, 1.5)

3

y = 6(0.5)3

(3, 0.75)

4

y = 6(0.5)4

(4, 0.375)

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 = 6(1/2)x.

answered Nov 25, 2014 by david Expert
0 votes

b)

The function y = 6(1/2)x

Compare it to exponential function y = abx

Since a = 6, y intercept of the function is 6.

answered Nov 25, 2014 by david Expert
0 votes

c)

y = 6(1/2)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, ∞).

answered Nov 25, 2014 by david Expert
0 votes

d) The function y = 6(1/2)x

y = 6(0.5)x

Compare it to exponential function y = abx

a = 6, b = 0.5

End behavior

Since b < 1, the function is decreasing.

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

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

answered Nov 25, 2014 by david Expert

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