Please help me out with this Algebra 1 question.
1 answer:
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Answer:
A - Not Function
B - Function
C - Function
D - Not Function
E - Function
Step-by-step explanation:
For a relation to be a function, each value of input should have exactly one output. Which means that for one value of x, there should only one value of y. If the relation has repetition of x in its ordered pairs, it means that for one value of x, there are two or more values of y, hence the relation is not a function
(Consult the diagram below)
<h3>A - {(6,12),(3,1),(−1,13),(6,4)} </h3>As x = 6 is being repeat, it means that x=6 has two values of y that are 12 and 4. IT IS NOT A FUNCTION.
<h3>B - {(−1,−2),(−4,−4),(0,−5),(7,−5)} </h3>No repetition of x, IT IS A FUNCTION.
<h3 /><h3>C - {(−5,1),(4,10),(5,10),(6,7)} </h3>No repetition of x, IT IS A FUNCTION.
<h3 /><h3>D - {(−1,4),(1,6),(−1,−2),(0,7)} </h3>As x = -1 is being repeat, it means that x=-1 has two values of y that are 4 and -2. IT IS NOT A FUNCTION.
<h3>E - {(−2,8),(2,1),(−4,8),(7,9)}</h3>No repetition of x, IT IS A FUNCTION.
For the given set of equations, the values of x = -8 and x = -2.
We have, f(x) = x² + 7x- 24 and g(x) = -3x - 40
An Equation is an algebraic statement that shows that two quantities are equal.
For one x-value of a solution,
We equate both the given functions,
Thus, f(x) = g(x)
x² + 7x- 24 = -3x - 40
+7x + 3x -24 + 40 = 0
+10x + 16 =0
+ 8x + 2x +16 =0
x(x+8) + 2(x +8) =0
(x+8) (x+2) = 0
x = -8 and x = -2
Hence, Concluding, we have x = -8 and x = -2
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