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3 years ago

According to the graph of F(x), which of the statements below are true? Check all that apply.

Mathematics

1 answer:

Nesterboy [21]3 years ago

7 0

The domain of the function is the value of the independent variable, or simply the x-values. The range is the value of the dependent variable, or the y-values. You can determine its domain and range if the curve of the function passes through their coordinates. Hence,

A. True. If you extend the curve downwards, its opening widens and would then encompass all x-values
B. True.
C. False. This is contradictory to A.
D. True. This is same with B.
E. False. This is contradictory to B.
F. False, the origin is at (0,2). It does not extend upward.

The answers are A, B and D.

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The graphs of g(x) = x³- ax² + 6 and h(x) = 2x² + bx + 3 touch when x = 1. Therefore, the tangent to

Olegator [25]

Answer:

$(1,\, 10)$ .

Step-by-step explanation:

Differentiate each function to find an expression for its gradient (slope of the tangent line) with respect to $x$ . Make use of the power rule to find the following:

$g^\prime(x) = 3\, x^2 - 2\, a\, x$ .

$h^\prime(x) = 2\, (2\, x) + b = 4\, x + b$ .

The question states that the graphs of $g(x)$ and $h(x)$ touch at $x = 1$ , such that $g^\prime(1) = h^\prime(1)$ . Therefore:

$3 - 2\, a = 4 + b$ .

On the other hand, since the graph of $g(x)$ and $h(x)$ coincide at $x = 1$ , $g(1) = h(1)$ (otherwise, the two graphs would not even touch at that point.) Therefore:

$1 - a + 6 = 2 + b + 3$ .

Solve this system of two equations for $a$ and $b$ :

$\begin{aligned}& a + b = 2 \\ & 2\, a + b = -1\end{aligned}$ .

Therefore, $a = -3$ whereas $b = 5$ .

Substitute these two values back into the expression for $g(x)$ and $h(x)$ :

$g(x) = x^3 + 3\, x^2 + 6$ .

$h(x) = 2\, x^2 + 5\, x + 3$ .

Evaluate either expression at $x = 1$ to find the $y$ -coordinate of the intersection. For example, $g(1) = 1 + 3 + 6 = 10$ . Similarly, $h(1) = 2 + 5 + 3 = 10$ .

Therefore, the intersection of these two graphs would be at $(1,\, 10)$ .

6 0

2 years ago

Step 1 choices:

Julli [10]

You have to translate the triangle over to where point B is lined up with point B in the second triangle. Then you can reflect over the y-axis.
So...your answer should be...
Step 1:A.
Step 2:C.

6 0

3 years ago

Read 2 more answers

A hiking trail is 2 3/5 miles long. Lucy walks 1/2 of the trail before stopping for a water break. How many miles does Lucy walk

Misha Larkins [42]

Answer:

look at the picture I have sent