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4 years ago

7

Write a linear function f with the values f(−1)=5 and f(3)=4.

1 answer:

Alexeev081 [22]4 years ago

7 0

You are given two points (-1,5), (3, 4)
find the slope: m=(4-5)/[3-(-1)]=-1/4
so you have y=(-1/4)x+b
use either point to find out b: 4=(-1/4)(3)+b =>b=19/4
the equation is y=(-1/4)x+19/4

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Which of these is an exponential function?

zhenek [66]

B and D. You are welcome.

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4 years ago

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sergejj [24]

Answer:

A

Step-by-step explanation:

We are given the function:

$\displaystyle f(x) = \left\{ \begin{array}{ll} 2\cos(\pi x) \text{ for } x \leq -1 \\ \\ \displaystyle \frac{2}{\cos(\pi x)}\text{ for } x > -1 \end{array} \right.$

And we want to find:

$\displaystyle \lim_{x\to -1}f(x)$

So, we need to determine whether or not the limit exists. In other words, we will find the two one-sided limits.

Left-Hand Limit:

$\displaystyle \lim_{x\to-1^-}f(x)$

Since we are approaching from the left, we will use the first equation:

$\displaystyle =\lim_{x\to -1^-}2\cos(\pi x)$

By direct substitution:

$=2\cos(\pi (-1))=2\cos(-\pi)=2(-1)=-2$

Right-Hand Limit:

$\displaystyle \lim_{x\to -1^+}f(x)$

Since we are approaching from the right, we will use the second equation:

$=\displaystyle \lim_{x\to -1^+}\frac{2}{\cos(\pi x)}$

Direct substitution:

$\displaystyle =\frac{2}{\cos(\pi (-1))}=\frac{2}{\cos(-\pi)}=\frac{2}{(-1)}=-2$

So, we can see that:

$\displaystyle \displaystyle \lim_{x\to-1^-}f(x)=\displaystyle \lim_{x\to -1^+}f(x) =-2$

Since both the left- and right-hand limits exist and equal the same thing, we can conclude that:

$\displaystyle \lim_{x \to -1}f(x)=-2$

Our answer is A.

8 0

3 years ago

5/2 (7x-15)+x>13/2-3/2

Evgen [1.6K]

5(7x - 15) + 2x ≥ 13x - 3 <em>multiplied both sides by 2 to clear the denominator</em>

35x - 75 + 2x ≥ 13 x - 3 <em>distributed 5 into 7x-15</em>

37x - 75 ≥ 13x - 3 <em>added like terms (35x and 2x)</em>

24x - 75 ≥ -3 <em>subtracted 13x from both sides</em>

24x ≥ 72 <em>added 75 to both sides</em>

x ≥ 3 <em>divided both sides by 24</em>

Answer: x ≥ 3 Notation: [3, ∞)

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3 years ago

Can someone help me pls?

Aleks [24]

The answer is number two

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3 years ago

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What is the equation of the line passing through the points (2/5, 19/20) and (1/3, 11/12) in slope-intercept form?

antiseptic1488 [7]

Answer: b is the answer

Step-by-step explanation:

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3 years ago