The graphs of f(x) = 10x and its translation, g(x), are shown. On a coordinate plane, 2 exponential functions are shown. f (x) a
pproaches y = 0 in quadrant 2 and increases into quadrant 1. It crosses the y-axis at (0, 1) and goes through (1, 10) and (2, 100). g (x) approaches y = 0 in quadrant 2 and increases into quadrant 2. It goes through (3, 1), (4, 10), and (5, 100). What is the equation of g(x)? g(x) = 10x – 3 g(x) = 10x + 3 g(x) = 10x – 3 g(x) = 10x + 3
2 answers:
Answer:
Detailed explanation:
* Let’s clarify the procedure for solving this problem
- An exponential function can be expressed as , where
a signifies the starting amount (x = 0), and b denotes the growth factor
- If b > 1, it qualifies as an exponential growth function
- If 0 < b < 1, it is categorized as an exponential decay function
- Horizontal translation to the right by h units results in the new function being
- Conversely, if translated to the left by h units, the function modifies to
- A vertical upward shift by k units alters the function to
- A vertical downward shift by k units means the new function accounts for
* Now, let’s solve the problem
∵ f(x) is an exponential function
∵ The points (0, 1), (1, 10), (2, 100) are points of f(x)
- g(x) is the transformation of f(x)
∵ The points (3, 1), (4, 10), (5, 100) belong to g(x)
∵ The point (0, 1) on f(x) transforms to (3, 1) on g(x)
∵ The point (1, 10) on f(x) transforms to (4, 10) on g(x)
∵ The point (2, 100) on f(x) translates to (5, 100) on g(x)
∵ Notably, all y-coordinates of f(x) match those of g(x)
indicating no vertical translation
∴ Hence, no vertical translation occurred
∵ The x-coordinates of f(x) are increased by
3 units to yield the x-coordinates for g(x)
∴ This shows that f(x) is translated 3 units to the right
∵
∴
- Refer to the corresponding graph for greater clarity
# The red curve denotes f(x)
# The blue curve signifies g(x)
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Answer:
(C) They have the same coefficient of variation
Step-by-step explanation:
The coefficient of variation (CV) is calculated using the formula:
Where represents standard deviation and
represents the mean.
Bob's average weight is 200 pounds with a standard deviation of 16 pounds
This indicates that .
Thus, his coefficient of variation is
Mary's average weight is 125 pounds, with a standard deviation of 10 pounds.
This implies
Therefore, her coefficient of variation is
Since both have the same coefficient of variation, the accurate response is.
(C) They have the same coefficient of variation