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3 years ago

9

Easy Points! Let f(x) represent a function. Which descriptions match the given transformations? Drag and drop the answers into t

he boxes.

1 answer:

Molodets [167]3 years ago

4 0

F(x)-4 : translated 4 units down
4f(x) : vertical stretched by a factor of 4

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What is the domain of g?

Mrac [35]

Answer:

Solution. The domain of g(x) consists of all real numbers except x = 32, since that input value would cause us to divide by 0. Likewise, the domain of f consists of all real numbers except 1. So we need to exclude from the domain of g(x) that value of x for which g(x) = 1.

Step-by-step explanation:

7 0

3 years ago

The minimum/maximum value of the function y = a(x − 2)(x − 1) occurs at x = d, what is the value of d?

daser333 [38]

Answer:

$d=\frac{3}{2}=1.5$

Step-by-step explanation:

We have the function:

$y=a(x-2)(x-1)$

And we want to find x=d for which the minimum/maximum value will occur.

Notice that our function is a quadratic in factored form.

Remember that the minimum/maximum value always occurs at the vertex point.

And remember that the x-coordinate of the vertex is the axis of symmetry.

Since a quadratic is always symmetrical on both sides of its axis of symmetry, a quadratic’s axis of symmetry is the average of the two roots/zeros of the quadratic.

Therefore, the value x=d such that it produces the minimum/maximum value is the average of the two roots.

Our factors are <em>(x-2) </em>and <em>(x-1)</em>.

Therefore, our roots/zeros are <em>x=1, 2</em>.

So, the average of them are:

$d=\frac{1+2}{2}=3/2=1.5$

Therefore, regardless of the value of <em>a</em>, the minimum/maximum value will occur at <em>x=d=1.5</em>.

Alternative Method:

Of course, we can also expand to confirm our answer. So:

$y=a(x^2-2x-x+2)\\y=a(x^2-3x+2)\\y=ax^2-3ax+2a$

The x-coordinate of the vertex is still going to be the place where the minimum/maximum is going to occur.

And the formula for the vertex is:

$x=-\frac{b}{2a}$

So, we will substitute <em>-3a</em> for <em>b</em> and <em>a</em> for <em>a</em>. This yields:

$x=-\frac{-3a}{2a}=\frac{3}{2}=1.5$

Confirming our answer.

4 0

3 years ago

Lyric spent half of his weekly allowance at the movies. To earn more money, his parents let him clean the windows in the house f

rusak2 [61]

Answer:

This question does not make since.

Step-by-step explanation:

7 0

3 years ago

What is the solution to the system of equations?

yarga [219]

Answer:

(2, - 4 )

Step-by-step explanation:

Given the 2 equations

x + 2y = - 6 → (1)

3x + y = 2 → (2)

Multiplying (2) by - 2 and adding to (1) will eliminate the term in y

- 6x - 2y = - 4 → (3)

Add (1) and (3) term by term to eliminate y

- 5x = - 10 ( divide both sides by - 5 )

x = 2

Substitute x = 2 into either of the 2 equations and solve for y

Substituting into (1)

2 + 2y = - 6 ( subtract 2 from both sides )

2y = - 8 ( divide both sides by 2 )

y = - 4

Solution is (2, - 4 )

8 0

4 years ago

jason runs 440 yards in 75 seconds. At this rate, how many minutes does it take him to run a mile? (1 mile = 1,760 yards).

mamaluj [8]

Answer:

5 minutes

Step-by-step explanation:

we know that

Jason runs 440 yards in 75 seconds

using proportion

Find out how many minutes does it take him to run a 1.760 yards (one mile)

$\frac{440}{75}=\frac{1,760}{x}\\\\x=1,760(75)/440\\\\x= 300\ sec$

Convert seconds to minutes

Divide by 60

$300\ sec=300/60=5\ min$

8 0

3 years ago