Find the domain and range of the relation and determine whether it is a function.

Mathematics

2 answers:

Over [174]2 years ago

7 0

A is the correct answer. If you write out the order pairs of each point the first number is your domain and the second number is your rang. Yes it is a function because your domain does not repeat.

Sergio [31]2 years ago

3 0

A is the correct answer. A function is defined where every input, x, has only one output. The coordinates are on the graph are (-4,-1), (-1,4), (1,1), and (4,1). As you can see, there is only one output for every input. X is the domain and y is the range.

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Could someone help me rnnn?

GuDViN [60]

Answer:

vertex = (0, -4)

equation of the parabola: $y=3x^2-4$

Step-by-step explanation:

Given:

y-intercept of parabola: -4
parabola passes through points: (-2, 8) and (1, -1)

Vertex form of a parabola: $y=a(x-h)^2+k$

(where (h, k) is the vertex and $a$ is some constant)

Substitute point (0, -4) into the equation:

$\begin{aligned}\textsf{At}\:(0,-4) \implies a(0-h)^2+k &=-4\\ah^2+k &=-4\end{aligned}$

Substitute point (-2, 8) and $ah^2+k=-4$ into the equation:

$\begin{aligned}\textsf{At}\:(-2,8) \implies a(-2-h)^2+k &=8\\a(4+4h+h^2)+k &=8\\4a+4ah+ah^2+k &=8\\\implies 4a+4ah-4&=8\\4a(1+h)&=12\\a(1+h)&=3\end{aligned}$