For this case, the parent function is given by:
We apply the following transformations:
Vertical translations:
Suppose that k> 0
To graph y = f (x) + k, move the graph of k units upwards:
For k = 9 we have:
Horizontal translations:
Suppose that h> 0
To graph y = f (x-h), move the graph of h units to the right
For h = 4 we have:
Answer:
The function g (x) is given by:
The path of the ball is an illustration of absolute equation.
The equation of the path is:
The given parameters are:
--- the vertex (i.e. the point where the ball hits the wall)
An absolute function is represented as:
Substitute
Substitute for x and y
Remove absolute bracket
Collect like terms
Solve for a
Simplify
Substitute in
Hence, the equation of the path is:
See attachment for graph that models the path
Read more about absolute equations at:
domain represents the x values so for example in a diagonal line that continues infinitely, the domain is all real numbers or (-infinity, infinity)
range represents y values so it would also be all real numbers or (-infinity, infinity)
let’s say there is a line (refer to pic) that moves ONLY from point (-3, -1) and (2, 2)
the domain would be [-3, 2]
we use brackets because it’s a real number unlike infinity (also because it’s a closed circle on the graph; if the graph had an open circle you would use a parenthesis)
and the range would be [-1, 2]
if you have any more questions about this explanation feel free to ask!
