2 years ago

Determine whether the relation is or is not a function.

Mathematics

1 answer:

soldier1979 [14.2K]2 years ago

5 0

Answer:

Not a function because it does not pass the Vertical Line Test.

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Find the smallest zero of f(x+5)

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ANSWER

1. k=13

2. x=-10

EXPLANATION

The given function is

$f(x) = {x}^{2} + 3x - 10$

To find f(x+5), plug in (x+5) wherever you see x.

This implies that:

$f(x) = {(x + 5)}^{2} + 3(x + 5) - 10$

Expand:

$f(x) = {x}^{2} + 10x + 25+ 3x + 15- 10$

Simplify to obtain

$f(x) = {x}^{2} + 13x + 30$

We now compare with,

$f(x) = {x}^{2} + kx + 30$

This implies that:

$k = 13$

To find the smallest zero of f(x+5), we equate the function to zero and solve for x.

${x}^{2} + 13x + 30 = 0$

${x}^{2} + 10x + 3x + 30 = 0$

$x(x + 10) + 3(x + 10) = 0$

$(x + 3)(x + 10) = 0$

$x = - 10 \: or \: x = - 3$

The smallest zero is -10.

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