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3 years ago

Select the correct answer. Which statement is correct with respect to f(x) = -3|x − 1| + 12?

Mathematics

1 answer:

professor190 [17]3 years ago

5 0

Answer:

Opt. D.

Step-by-step explanation:

To solve this problem we need to focus our attention in the abs(x-1) function,

If x>1, then abs|x-1|= x-1, if x<1 then abs|x-1|= 1-x. And in the two intervals, the function opens upwards.

But our function has -3 multiplying abs|x-1|, This means that our function opens downward.

The vertex point can be found when x=1, since abs(x-1)=0. this gives f(1)=12

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Evaluate 5÷9(F - 32) when f=50

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2 years ago

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The graph of y=x^3 is transformed as shown in the graph below. Which equation represents the transformed function?

omeli [17]

Answer:

y = (-x)^3 - 4

Step-by-step explanation:

Ok, for the function:

y = x^3

When x = 0, we have:

y = 0^3 = 0

So the original graph passes through the point (0, 0)

If we look at the given graph, we can see that the y-intercept (the value of y when x = 0) is:

y = -4

So, this is the graph of y = x^3 moved down 4 units.

You can also see that the graph goes downward as x increases (and up as x decreases) while for the function:

y = x^3

as x increases, we should see that y also increases.

Then we have a reflection across the x-axis.

Ok, now let's describe a vertical shift.

For a general function f(x), a vertical shift of N units is written as:

g(x) = f(x) + N

if N is positive, the shift is upwards

if N is negative, the shift is downwards.

And for a function f(x), a reflection across the x-axis is written as:

g(x) = - f(x)

Here we first apply the reflection across the x-axis, so we get:

g(x) = -f(x)

now we apply the shift 4 units downwards

g(x) = - f(x) - 4

replacing f(x) by our function, x^3

we get:

g(x) = -x^3 - 4

And because of the odd power, we can write:

-x^3 = (-x)^3

Then the function is:

g(x) = (-x)^3 - 4

The correct option is the last one.

y = (-x)^3 - 4

3 0

3 years ago

Which graph shows the solution to the system of linear inequalities?<br> y< 2x-5<br> y>-3x + 1

trapecia [35]

Answer:

See explanation

Step-by-step explanation:

Plot the solution sets to both inequalities.

1. For the inequality $y$ First, plot the dotted line $y=2x+5$ (dotted because sign is without notion "or equal to"), then choose correct part by substitution coordinates of the origin.

$2\cdot 0-5=-5$

so the origin does not belong to the needed part. Shade the part, which does not include origin.

2. For the inequality $y>-3x+1.$ First, plot the dotted line $y=-3x+1$ (dotted because sign is without notion "or equal to"), then choose correct part by substitution coordinates of the origin.