identify the graph as a translation of a basic function and write the formula for the graph

Question

on the graph it is a single line moving slightly up and to the right

starting

3,0

4,1

5,1.5

6,1.75

7.2

then I need to figure out the basic function of y=

formula for the graph: y=

Answer 1

I am assuming that (3,0), (4,1), (5, 1.5), (6,1.75) and (7,2)

are not exact points taken from a table, but rather points inferred from reading a graph.

(Not what I originally assumed, so this is not my original answer.😊)

In that case (5, 1.5) and (6,1.75) are just estimates while (3,0), (4,1), and (7,2) are the only points known exactly. An easily found function that passes through (3,0), (4,1), and (7,2) is y = √(x – 3).

It’s not too difficult to imagine the points (5, √2) and (6, √3) read off a graph being estimated as (5, 1.5) and (6,1.75).

Answer

My new, much shorter, answer is:

The basic function of y: y = √(x)

The formula for the graph is y: y = √(x – 3).

Note

y = √(x – 3) is the basic function translated 3 units to the right.

Answer 2

the graph you are describing

is

y=(1/24)x³-(3/4)x²+(113/24)x-(17/2)

The key to knowing the data indicates cubic is the differences of differences of differences is constant when x is increasing by unit intervals.

Need five points to calculate and the constant is .25, yay, data indicates cubic.

now need four points to calculate

a,b,c,d

for y=ax³+bx²+cx+d

using four points, have 4x4 matrix equation. I went to Wolfram alpha to solve.

j