Which function is increasing?
a. y = -2^x
b. y = 2 (1/2^x)
c. y = 3 (4^-x)
d. y = -4 (2^x)
What is the y-intercept of the function y = 4(2^x) - 2?
a. 2
b. -2
c. 4
d. 1
In the function y = 4(3^x) - 1, the graph is asymptotic to .....
a. y = 1
b. y - axis
c. y = -1
d. x - axis
#1, none are increasing
http://www.wolframalpha.com/input/?i=plot+y+%3D+-2%5Ex+%2C+y+%3D+2+%281%2F2%5Ex%29+%2C+y+%3D+3+%284%5E-x%29+%2C+y+%3D+-4+%282%5Ex%29
2. for y-intercept , let x = 0
4(2^0) - 2
= 4(1) - 2
= 2
3. as x ---> +big 3^x get big , so the whole expression becomes larger and larger, thus no asymtpote there.
as x ----> -big, 3^x gets smaller and smaller
and the first term will become zero, leaving you with y = -1
To determine which function is increasing, we need to look at the exponent and the coefficient of the base in each function.
a. y = -2^x: This function has a negative coefficient (-2) and a positive exponent (x). Therefore, it is a decreasing function.
b. y = 2 (1/2^x): The exponent in this function is negative (-x). When the exponent is negative, the function is increasing since its value gets smaller as x increases.
c. y = 3 (4^-x): The coefficient in this function is positive (3), and the exponent is negative (-x). Just like in the previous case, when the exponent is negative, the function is increasing.
d. y = -4 (2^x): This function has a negative coefficient (-4) and a positive exponent (x). Therefore, it is a decreasing function.
Therefore, the functions that are increasing are option b (y = 2 (1/2^x)) and option c (y = 3 (4^-x)).
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To find the y-intercept of the function y = 4(2^x) - 2, we set x to 0 and solve for y.
Plugging in x = 0:
y = 4(2^0) - 2
y = 4(1) - 2
y = 4 - 2
y = 2
So the y-intercept is 2. Therefore, the correct answer is option a (2).
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To determine what the graph of the function y = 4(3^x) - 1 is asymptotic to, we need to analyze the behavior as x approaches positive and negative infinity.
As x approaches negative infinity, the exponent 3^x approaches 0, making the function approach -1. Therefore, the graph is asymptotic to the line y = -1 as x approaches negative infinity.
As x approaches positive infinity, the exponent 3^x increases exponentially, making the function approach positive infinity. Therefore, the graph is not asymptotic to any line as x approaches positive infinity.
So the correct answer is option c (y = -1).