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Karo-lina-s [1.5K]

2 years ago

9

Graph each piecewise function. Then identify the properties.

1 answer:

soldier1979 [14.2K]2 years ago

7 0

Answer:

Domain: (-∞, 0] U (0, ∞): All real numbers.

Range: (-∞, ∞)

Step-by-step explanation:

This function is composed of two polynomial functions, a quadratic whose domain is all real numbers and a negative slope whose domain is all real numbers.

Observe in the attached graph that the function is continuous for the whole domain, it does not have any jump. In addition, the parabolic function comes from ∞, then it has a minimum value in y = 1 it grows up to y = 4. Finally it joins with the equation of the line and it extends to -∞.

Then we can conclude that for this piecewise function:

Domain: (-∞, 0] U (0, ∞): All real numbers.

Range: (-∞, ∞)

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inysia [295]

Answer:

D. The graph of function $g$ is the graph of function $f$ shifted 4 units to the left.

Step-by-step explanation:

the function $g$ is composite function between $f$ and $x + 4$ , then you can re-write $g$ as:

$g(x) = 10^{x+4}$

The transformation happened in the input, then you have an horizontal shifted and how it's adding 4 units then you go "faster" and move to left the graph.

In the image you can see what's mean sum a constant in the $x$ of a function.

8 0

2 years ago

Solve sin2x=-1/2 on the interval 0≤ angle≤360°

GREYUIT [131]

Answer:

x=135

Step-by-step explanation:

We know that sin(270) = -1/2

So 2x = 270

x = 135

8 0

2 years ago

Find the exponential equation, y equals a times b to the x power (y= a(b^x)), of the exponential function containing the points

guajiro [1.7K]

Y=4 (6^x)

comment if you want me to explain it

5 0

3 years ago

Noah spent $66 for 20 gallons of gasoline. Lydia spent $81.25 for 25 gallons of gasoline. How much did each person spend for 1 g

Morgarella [4.7K]

Answer:

Noah spent $3.3 for 1 gallon of gasoline.

Lydia spent $3.25 for 1 gallon of gasoline.

Step-by-step explanation:

To find how much each person spent for 1 gallon of gasoline, we divide the amount spent by the number of gallons.

Noah spent $66 for 20 gallons of gasoline.

Amount spent $66, 20 gallons. So

66/20 = $3.3

Noah spent $3.3 for 1 gallon of gasoline.

Lydia spent $81.25 for 25 gallons of gasoline.

Amount spent $81.25, 25 gallons. So

81.25/25 = $3.25

Lydia spent $3.25 for 1 gallon of gasoline.

7 0

2 years ago

Use the quadratic formula to solve the equation.

Sergeeva-Olga [200]

ANSWER

$x = \frac{ 5 - \sqrt{ 5} }{4} \: or \: \: x = \frac{ 5 + \sqrt{ 5} }{4}$

EXPLANATION

The given quadratic equation is

$4 {x}^{2} - 10x + 5 = 0$

We compare this to

$a {x}^{2} + bx + c = 0$

to get a=4, b=-10, and c=5.

The quadratic formula is given by

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

We substitute these values into the formula to get:

$x = \frac{ - - 10 \pm \sqrt{ {( - 10)}^{2} - 4(4)(5)} }{2(4)}$

This implies that

$x = \frac{ 10 \pm \sqrt{ 100 - 80} }{8}$

$x = \frac{ 10 \pm \sqrt{ 20} }{8}$

$x = \frac{ 10 \pm2 \sqrt{ 5} }{8}$

$x = \frac{ 5 \pm \sqrt{ 5} }{4}$

The solutions are:

$x = \frac{ 5 - \sqrt{ 5} }{4} \: or \: \: x = \frac{ 5 + \sqrt{ 5} }{4}$

7 0

2 years ago

Read 2 more answers