Using translation concepts, the graph of f(x) = (x - 2)² + 3 is given at the end of the question.
<h3>What is a translation?</h3>
A translation is represented by a change in the function graph, according to operations such as multiplication or sum/subtraction either in it’s definition or in it’s domain. Examples are shift left/right or bottom/up, vertical or horizontal stretching or compression, and reflections over the x-axis or the y-axis.
In this problem, we have that the parent and the translated function are given, respectively, by:
The translations are as follows:
- Right two units, as x -> x - 2.
- Up 3 units, because f(x) = g(x) + 3.
Hence the graphs are given at the end of the answer, with the parent function in red and the translated function f(x) = (x - 2)² + 3 in green.
More can be learned about translation concepts at brainly.com/question/4521517
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Answer:
<h2>B) 0</h2>
Step-by-step explanation:
The slope of a horizontal line is equal to 0.
The slope of a vertical line is undefined.
The formula of a slope:
Put the coordinates of the pojnts from the graph (2, 9) and (4, 9):
Answer:
6
Step-by-step explanation:
15-9
Answer:
Jessica scored 835 points,
and Tina scored 717 points.
Step-by-step explanation:
Let $j$ stand for Jessica Bradley, and let $t$ stand for Tina Harner. By turning the words of this problem into equations, we get:
j - 118 = t
and, j + t = 1552.
Now that we have a system of equations, all we have to do now is to solve it.
By substituting the value of t (first equation) into the second equation, we get:
j + (j - 118) = 1552.
Get rid of the parentheses:
j + j - 118 = 1552
Simplifing:
2j - 118 = 1552
2j = 1670
j = 835.
Now that we know how many points Jessica scored, we can easily find out how many points Tina scored. By sticking in the value of Jessica's score into the first equation.
835 - 118 = t
t = 717.
So, the answer to this problem is (j, t) = (835, 717).
Answer:
The correct answer is A) It has rotational symmetry about the origin.
Step-by-step explanation:
In principle, the graph of an odd function is symmetric with respect to the origin. This simply means that the point (0 ,0) acts as a mirror line to the function so that one half of the function looks exactly like the other half when reflected over the origin.
A function f(x) is said to be odd if and only if;
f(-x) = -f(x)
The ultimate example of an odd function is the sine function. Consider the function below;
f(x) = sin(x)
Then;
f(-x) = sin(-x) = -sin(x) = -f(x)
Working with actual values;
sin(-30) = -sin(30) = -0.5
A graph of the function f(x) = sin(x) is shown in the attachment below;
If the graph is rotated about the origin, we would still end up with the same graph.
In summary, an odd function is symmetric with respect to the origin and has rotational symmetry about the origin.