A dolphin is swimming to the surface of the ocean while at the same time a bird is flying towards the surface of the ocean. The
function fx) models the position, in feet, of the dolphin x seconds after it starts swimming towards the surface. The function models the dolphin's position for the first 5 seconds The function g (x) models the position, in feet, of the bird x seconds after the bird begins flying towards the surface. The function models the bird's position for the first 5 seconds. A partial table of values for the two linear functions is shown. x f (x) g (x) 0.0-11 10 0.59 9 1.07 8 1.55 7 2.0 -3 6 2.5 -1 5 After how many seconds will the dolphin and bird be at the same position?
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There is no absolute value function when graphed, will be wider than the graph of the parent function f(x) = |x|
<h3>What is an absolute value function?</h3>An absolute value function is a function such that,
For the given example,
We have been given a parent function f(x) = |x|
We need to find the absolute value function, when graphed, will be wider than the graph of the parent function.
Consider the graph of all absolute value functions.
The graph of f(x) = |x| + 3 is represented blue color.
The graph of f(x) = |x − 6| is represented green color.
The graph of f(x) = |x| is represented red color.
The graph of f(x) = 9|x| is represented violet color.
From this graph, we can observe that,
f(x) = |x| + 3 is as wise as the parent absolute value function f(x) = |x| translated up by 3 units.
Similarly, the function f(x) = |x - 6| is as wise as the parent absolute value function f(x) = |x| translated right by 6 units.
This means, there is no absolute value function when graphed, which will be wider than the graph of the parent function f(x) = |x|
Learn more about the absolute value function here:
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