4 years ago

Is the following relation a function? (4,2), (1,1), (0,0), (1, -1), (4, -2). Give the domain and range.

Mathematics

1 answer:

natima [27]4 years ago

8 0

It's not a function because 4 and 1 has 2 images in y so there's no range but the domain = {4,1,0}

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denpristay [2]

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3 years ago

Read 2 more answers

Use the Rational Zero Theorem to list all possible rational zeros for the given function. f(x) = 10x^5 + 8x^4 - 15x^3 +2x^2 - 2

vagabundo [1.1K]

Given:

The function is:

$f(x)=10x^5+8x^4-15x^3+2x^2-2$

To find:

All the possible rational zeros for the given function by using the Rational Zero Theorem.

Solution:

According to the rational root theorem, all the rational roots are of the form $\dfrac{p}{q},q\neq 0$ , where p is a factor of constant term and q is a factor of leading coefficient.

We have,

$f(x)=10x^5+8x^4-15x^3+2x^2-2$

Here,

Constant term = -2

Leading coefficient = 10

Factors of -2 are ±1, ±2.

Factors of 10 are ±1, ±2, ±5, ±10.

Using the rational root theorem, all the possible rational roots are:

$x=\pm 1,\pm 2,\pm \dfrac{1}{2}, \pm \dfrac{1}{5},\pm \dfrac{2}{5},\pm \dfrac{1}{10}$ .

Therefore, all the possible rational roots of the given function are $\pm 1,\pm 2,\pm \dfrac{1}{2}, \pm \dfrac{1}{5},\pm \dfrac{2}{5},\pm \dfrac{1}{10}$ .