Explain in sentences what a translations in, then create your own function and show 2 different translations – explain what each translation you create does to the parent graph.

Okay when you start with a parent graph

y = |x|   you can translate it

y = |x|  + 5  the number outside moves it up and down vertically

y =  |x - 6|  the -6 moves it right and left opposite to -6 (it moves it +6)

y = 3|x|  the 3 stretches or compresss it vertically (it gets skinnier or fatter)

This can be done with all types of graphs

y = x²

y= 2(x-3)² - 7  this is move +3 right, down 7 and stretched by 2

b. 1.25 hr

step-by-step explanation:

if you have a constant speed of 60 mph, then you have a ratio between 60 mi. to 1 hr. dividing both sides by 60 we get the ratio

1 mi. to

then mult. both sides by 75 we get the ratio

75 mi. to

simplifying we get

75 mi. to

or 1.25 hr.

p ÷ r = tan(x)

step-by-step explanation:

given that there is a figure below shows a right triangle: a right triangle is shown with hypotenuse equal to q units and the length of the legs equal to p units and r units.

graph is missing so i will create the graph as per given information.

the angle between the legs having lengths p units and q units is y degrees. the angle between the legs having lengths r units and q units is x degrees.

now we need to find about what is p ÷ r equal to.

so we can use trigonometric ratio tan(x)=[altitude]/[base] to find the value of p ÷ r, because p is the altitude and r is the base.

p ÷ r=tan(x)

hence final answer is p ÷ r=tan(x).