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3 years ago

Is the function even, odd, or neither?

Mathematics

2 answers:

Step2247 [10]3 years ago

3 0

Answer:

A function with a graph that is symmetric about the origin is called an odd function. Note: A function can be neither even nor odd if it does not exhibit either symmetry. For example, f(x)=2x f ( x ) = 2 x is neither even nor odd.

Step-by-step explanation:

enot [183]3 years ago

3 0

You may be asked to "determine algebraically" whether a function is even or odd. To do this, you take the function and plug –x in for x, and then simplify. If you end up with the exact same function that you started with (that is, if f (–x) = f (x), so all of the signs are the same), then the function is even. If you end up with the exact opposite of what you started with (that is, if f (–x) = –f (x), so all of the signs are switched), then the function is odd.

In all other cases, the function is "neither even nor odd".

Let's see what this looks like in action:

Determine algebraically whether f (x) = –3x2 + 4 is even, odd, or neither.

If I graph this, I will see that this is "symmetric about the y-axis"; in other words, whatever the graph is doing on one side of the y-axis is mirrored on the other side:

graph of y = –3x^2 + 4

This mirroring about the y-axis is a hallmark of even functions.

Also, I note that the exponents on all of the terms are even — the exponent on the constant term being zero: 4x0 = 4 × 1 = 4. These are helpful clues that strongly suggest to me that I've got an even function here.

But the question asks me to make the determination algebraically, which means that I need to do the algebra.

So I'll plug –x in for x, and simplify:

f (–x) = –3(–x)2 + 4

= –3(x2) + 4

= –3x2 + 4

I can see, by comparing the original function with my final result above, that I've got a match, which means that:

f (x) is even

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You want to know the type of music listened to by 15- to 20-year-olds. Which of the following surveys is biased?

Liula [17]

Arguably, all of them are at least somewhat biased, but the most biased would be surveying people 15 to 20 years old leaving a concert because being at a concert would be highly correlated with liking the type of music played at that concert.

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3 years ago

Please help me!!!!!

chubhunter [2.5K]

Answer:

y = - $\frac{2}{5}$ (x - 5)² + 7

Step-by-step explanation:

The equation of a quadratic in vertex form is

y = a(x - h)² + k

where (h, k ) are the coordinates of the vertex and a is a multiplier

Here (h, k ) = (5, 7 ) , then

y = a(x - 5)² + 7

To find a substitute (10, - 3 ) into the equation

- 3 = a(10 - 5)² + 7 ( subtract 7 from both sides )

- 10 = 5²a = 25a ( divide both sides by 25 )

$\frac{-10}{25}$ = a , that is

a = - $\frac{2}{5}$

y = - $\frac{2}{5}$ (x - 5)² + 7 ← in vertex form

8 0

3 years ago

A person on tour has dollar 360 for his daily expenses. If he extends his tour for 4 days, he has to cut down his daily expenses

mash [69]

Answer:

The original duration of the tour = 20 days

Step-by-step explanation:

Solution:

Total expenses for the tour = $360

Let the original tour duration be for $x$ days.

So, for $x$ days the total expense = $360

Thus the daily expense in dollars can be given by = $\frac{360}{x}$

Tour extension and effect on daily expenses.

The tour is extended by 4 days.

Tour duration now = $(x+4)$ days

On extension, his daily expense is cut by $3

New daily expense in dollars = $(\frac{360}{x}-3)$

Total expense in dollars can now be given as: $(x+4)(\frac{360}{x}-3)$

Simplifying by using distribution (FOIL).

$(x.\frac{360}{x})+(x(-3)+(4.\frac{360}{x})+(4(-3))$

$360-3x+\frac{1440}{x}-12$

$348-3x+\frac{1440}{x}$

We know total expense remains the same which is = $360.

So, we have the equation as:

$348-3x+\frac{1440}{x}=360$

Multiplying each term with $x$ to remove fractions.

$348x-3x^2+1440=360x$

Subtracting $348x$ both sides

$348x-348x-3x^2+1440=360x-348x$

$-3x^2+1440=12x$

Dividing each term with -3.

$\frac{-3x^2}{-3}+\frac{1440}{-3}=\frac{12x}{-3}$

$x^2-480=-4x$

Adding $4x$ both sides.

$x^2+4x-480=-4x+4x$

$x^2+4x-480=0$

Solving using quadratic formula.

For a quadratic equation: $ax^2+bx+c=0$

$x=\frac{-b\pm\sqrt{b^2-4ac}}{2a}$

Plugging in values from the equation we got.

$x=\frac{-4\pm\sqrt{(4)^2-4(1)(-480)}}{2(1)}$

$x=\frac{-4\pm\sqrt{16+1920}}{2}$

$x=\frac{-4\pm\sqrt{1936}}{2}$

$x=\frac{-4\pm44}{2}$

So, we have

$x=\frac{-4+44}{2}$ and $x=\frac{-4-44}{2}$

$x=\frac{40}{2}$ and $x=\frac{-48}{2}$

∴ $x=20$ and $x=-24$

Since number of days cannot be negative, so we take $x=20$ as the solution for the equation.

Thus, the original duration of the tour = 20 days

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3 years ago

Given f(x) = –7x + 9 and h(x) = –5(–7x + 9), what are the slope and y-intercept of the graph of function h?

taurus [48]

The Slope of f(x) = –7x + 9 is (-7)

The slope of h(x) = –5(–7x + 9) is (35)

The y-int of h(x) is (-45).

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Last week, a coral reef grew 19.8mm taller. How much did it grow in meters?

Oliga [24]

Answer:

Last week the coral reef grew .0196m

Step-by-step explanation:

So it's hard to explain but simply Milli witch is the symbol "m" is a unit prefix in the metric system denoting a factor of one thousandth (10 −3). So 19.6mm is 19.6*10^-3m. in other words 19.6 times 10^-3m

hope this helps sorry it's so complicated :/

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3 years ago

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