The result concluded is equivalent to a single rotation transformation of the original object.
<h3>Explanation of how reflection across axis works?</h3>
When a graph is reflected along an axis, say x-axis, then that leads the graph to go just on the opposite side of the axis as if we're seeing it in a mirror.
The Compositions of Reflections Over Intersecting Lines states that if we perform a composition of two reflections over two lines that intersect.
The result concluded is equivalent to a single rotation transformation of the original object.
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In order to answer this question, we must break this mathematical expression up into a series of mathematical operations (exponent, multiplication,division, addition, and/or subtraction):
"4 times a number" - The word "times" implies that we have to multiply 4 by an unknown number. We can simply label this unknown number as x.
"cubed" - In order to "cube" a number, we must raise it to the third power, or have an exponent of 3. Our unknown number of x now becomes x3 because we raised it to the third power.
"decreased by 7" - The word "decreased" implies that we must subtract 7 from the product of 4 multiplied by x3
With all of the information we now have, we can form an algebraic expression for this problem.
"4 times a number cubed decreased by 3" now becomes:
4x3 - 7
Answer:
Step-by-step explanation:
The input-output table can be made by putting value of x and finding the value of f(x)
f(x) = 3x^2-x+4
f(0) = 3(0)^2-0+4 = 0-0+4 = 4
f(1) = 3(1)^2-1+4 = 3-1+4 = 2+4 =6
f(2) = 3(2)^2-2+4 = 3(4)-2+4 = 12-2+4 = 10+4 = 14
f(3) = 3(3)^2-3+4 = 3(9)-3+4 = 27-3+4 = 24+4 = 28
So put value of x and find f(x) and fill the input-output table.
x f(x)
0 4
1 6
2 14
3 28
