Vhich of the following functions have graphs that oscillate? Select all that apply

Mathematics

1 answer:

gladu [14]3 years ago

6 0

Answer:

Only options A and B are correct, i.e. y = sin∅ and y = cos∅.

Step-by-step explanation:

The graphs that oscillate, should be periodic in nature and continuous functions.

We know all trigonometric functions are periodic in nature. But not all trigonometric functions are continuous.

The function is continuous if its values are defined at all angles and it should not be undefined for any particular angle.

We know the following facts:-

tan(90°) = ∞

sec(90°) = ∞

csc(0°) = ∞

cot(0°) = ∞

<u>Only sin and cos don't have values ∞ at any angle.</u> It means only sin and cos are continuous functions.

Hence, only options A and B are correct, i.e. y = sin∅ and y = cos∅.

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What is the value of x?

BlackZzzverrR [31]

We can use the Pythagorean theorum

a^2+b^2=c^2

c^2 is the length of the longest side squared

so

6^2 + b^2 = 10^2

36+ b^2 = 100
-36 -36

b^2 = 64

b = 8

b is the same thing as your "x", so x = 8

7 0

3 years ago

Read 2 more answers

suppose f(x)=3x+5. describe how the graph of each function compares to f. 1) g(x)=f(x)+12 2) h(x)=f(x)-7 3) g(x)=f(x=8) 4) h(x)=

Lubov Fominskaja [6]

g(x) = f(x)+12 represents translating f(x) 12 units up to get g(x). This is because y = f(x), so we're effectively adding 12 to each y coordinate of the points on f(x) to have them move to the points on g(x).

note: the term "translating" is another way of saying "shifting" or "sliding".

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h(x) = f(x)-7 means translating f(x) 7 units down to get h(x). We use the same reasoning as in problem 1. The general form is h(x) = f(x)+k, and in this case, k = -7. The negative k value tells us to shift down.

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g(x) = f(x+8) means we translate 8 units to the left. The general template is g(x) = f(x-h). If h > 0, then we shift right. If h < 0, then we shift left. The amount that is shifted is equal to the absolute value of h.

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h(x) = f(x-14) tells us to shift f(x) 14 units to the right. Same idea as problem 3, but now h = 14.

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g(x) = 4*f(x) means we vertically stretch f(x) by a factor of 4. Since y = f(x), we are effectively doing g(x) = 4*f(x) = 4*y, which pulls the y coordinates upward by a factor of 4. A point like (1,2) will jump to (1,8) after multiplying the y coordinate by 4.

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g(x) = f(5x) tells us to horizontally compress f(x) by a factor of 5. The general template is g(x) = f(a*x) where the 'a' determines horizontal stretching or compression. If $0 \le a \le 1$ , then we have horizontal stretching going on. If $a > 1$ , then we'll have horizontal compression.