Mathematics, 28.01.2020 10:31 ssuereichard

What value represents the horizontal translation from the graph of the parent function f(x) = x2 to the graph of the function g(x) = (x – 4)2 + 2?

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Answer from: bunbun2913

The value of horizontal shift is that means graph of parent function is shifted to right by 4 units.

Step-by-step explanation:

We have been given a parent function f(x)=x^2 and another function g(x)=(x-4)^2+2 . We are asked to determine the horizontal translation from the graph of the parent function to the graph of the function g(x).

Let us recall translation rules.

Horizontal translation:

$f(x)\rightarrow f(x-a)=\text{Graph shifted to the right by 'a' units}$

$f(x)\rightarrow f(x+a)=\text{Graph shifted to the left by 'a' units}$

Vertical translation:

$f(x)\rightarrow f(x)-a=\text{Graph shifted downwards by 'a' units}$

$f(x)\rightarrow f(x)+a=\text{Graph shifted upwards by 'a' units}$

Upon looking at our both functions, we can see that parent function is shifted to right by 4 units and upwards by 2 units to get the the function g(x).

Therefore, the value of horizontal translation is , which indicates the graph is shifted to right by 4 units.

Answer from: Quest

image result for what is another name for consecutive interior angles?

when two lines are crossed by another line (called the transversal): the pairs of angles on one side of the transversal but inside the two lines are called consecutive interior angles. in this example, these are consecutive interior angles: d and f.

step-by-step explanation:

Answer from: Quest

$y> \frac{1}{3}x$ and y≤ -x +4 .

step-by-step explanation:

we are given a graph for system of inequalities.

in order to write the system of inequalities for the given graph, we need to find the inequality for each of the line separately.

let us find the slope of dotted line first.

taking two coordinates on the graph.

let us say (0,0) and (3,1).

let us find the slope of the line now.

slope of the dotted line would be = $\frac{1-0}{3-0} = \frac{1}{3}$ .

y-intercept of dotted line is y=0 only.

plugging slope m= $\frac{1}{3}$ and b=0 in slope-intercept form y=mx+b, we get

$y=\frac{1}{3}x$ .

the line is shaded up of that dotted line.

therefore, for shading up we would take greater than inequality symbol > .

and because it's a dotted line we would take only > symbol in place of = sign in above equation of line.

therefore, inequality for dotted line would be

$y> \frac{1}{3}x$ .

let us take two points (3,1) and (0,4) on the solid line.

slope of the solid line would be = $\frac{4-1}{0-3} = \frac{3}{-3}=-1$ .

for the solid line we have y-intercept b= 4.

plugging slope m= -1 and b=4 in slope-intercept form y=mx+b, we get

y = -1x + 4.

the line is shaded down of that solid line.

therefore, for shading down we would take less than inequality symbol < .

and because it's a solid line we would take ≤ symbol in place of = sign in above equation of line.

therefore, inequality for solid line would be

y≤ -x +4 .
Write a system of inequalities to represent the shaded portion of the graph.

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What value represents the horizontal translation from the graph of the parent function f(x) = x2 to...

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