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4 years ago

Find the range of the given function f(x)=(x-1)^2+1

Mathematics

1 answer:

alexgriva [62]4 years ago

5 0

Answer:

a.) [1, infinity)

Step-by-step explanation:

The equation is that of a parabola that opens upward with vertex (1, 1). Hence the minimum value of f(x) is 1, and all values greater than that are part of the range: [1, ∞).

_____

The "vertex form" of the equation of a parabola is ...

f(x) = a(x -h)^2 + k

The vertex is at (h, k). When a > 0, the parabola opens upward. When a < 0, the parabola opens downward. Whichever way it opens, the value k is an extreme value and the limit of the range.

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Direct variation worksheet

vaieri [72.5K]

Answer:

Part 4) k=1/2

Part 5) k=-2/3

Part 6) y=32

Part 7) x=6

Part 8) v=99

Part 9)b=6

Part 10) y=6

Step-by-step explanation:

we know that

A relationship between two variables, x, and y, represent a proportional variation if it can be expressed in the form $y/x=k$ or $y=kx$

In a proportional relationship the constant of proportionality k is equal to the slope m of the line and the line passes through the origin

Part 4) Find the value of the constant of proportionality k

we have

$y=\frac{1}{2}x$

Remember that the value of k is the same that the value of the slope

$m=\frac{1}{2}$

$k=\frac{1}{2}$

Part 5) Find the value of the constant of proportionality k

we have

$y=-\frac{2}{3}x$

Remember that the value of k is the same that the value of the slope

$m=-\frac{2}{3}$

$k=-\frac{2}{3}$

Part 6) Suppose that y varies directly with x, and y=16 when x=8. Find y when x=16

step 1

Find the value of the constant of proportionality k

$k=y/x$

$k=16/8=2$

step 2

Find the equation of the direct variation

$y=kx$

substitute the value of k

$y=2x$

step 3

Find y when x=16

$y=2(16)=32$

Part 7) Suppose that y varies directly with x, and y=21 when x=3. Find x when y=42

step 1

Find the value of the constant of proportionality k

$k=y/x$

$k=21/3=7$

step 2

Find the equation of the direct variation

$y=kx$

substitute the value of k

$y=7x$

step 3

Find x when y=42

$42=7x$

solve for x

$x=42/7$

$x=6$

Part 8) Suppose that v varies directly with g, and v=36 when g=4. Find v when g=11

step 1

Find the value of the constant of proportionality k

$k=v/g$

$k=36/4=9$

step 2

Find the equation of the direct variation

$v=kg$

substitute the value of k

$v=9g$

step 3

Find v when g=11

$v=9(11)=99$

Part 9) Suppose that a varies directly with a, and a=7 when b=2. Find b when a=21

step 1

Find the value of the constant of proportionality k

$k=a/b$

$k=7/2=3.5$

step 2

Find the equation of the direct variation

$a=kb$

substitute the value of k

$a=3.5b$

step 3

Find b when a=21

$21=3.5b$

solve for b

$b=21/3.5$

$b=6$

Part 10) Suppose that y varies directly with x, and y=9 when x=3/2. Find y when x=1

step 1

Find the value of the constant of proportionality k

$k=y/x$

$k=9/(3/2)=6$

step 2

Find the equation of the direct variation

$y=kx$

substitute the value of k

$y=6x$

step 3

Find y when x=1

$y=6(1)=6$

6 0

4 years ago

Solve pls <br> 2x - 5 = 7

storchak [24]

Answer:

Step-by-step explanation:

$2x - 5 = 7 \\ 2x = 12 \\ x = 6$

4 0

3 years ago

Read 2 more answers

PlZ help I need an answer I don't need to waste points so plz Help!!!!!!!!!

nadya68 [22]

Answer:

The first obe

Step-by-step explanation:

5 0

4 years ago

Read 2 more answers

What is f(x)=x3+2x2−5x−6 in factored form given that 2 is a zero of the function?

murzikaleks [220]

Answer:

Since 2 or x-2= 0 is a zero of the function we divide it by the function to get the other factors

x³ + 2x² - 5x - 6 ÷ x -2

We get

(x + 3)(x+1) = 0

Therefore x³ + 2x² - 5x - 6 in factored form is

(x - 2)(x + 3)(x + 1)

Hope this helps.

4 0

4 years ago

Read 2 more answers

You just have to find x. please help been stuck for so long.

zzz [600]

Answer:

x = 84°

Step-by-step explanation:

The inscribed angle x is half the measure of the intercepted arc, that is

x = 0.5 × 168° = 84°

5 0

3 years ago