What is the slope of a line that is parallel to the line represented by the equation y=7/6x+4
1 answer:
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Answer:
Step-by-step explanation:
When a question asks for the "end behavior" of a function, they just want to know what happens if you trace the direction the function heads in for super low and super high values of x. In other words, they want to know what the graph is looking like as x heads for both positive and negative infinity. This might be sort of hard to visualize, so if you have a graphing utility, use it to double check yourself, but even without a graph, we can answer this question. For any function involving x^3, we know that the "parent graph" looks like the attached image. This is the "basic" look of any x^3 function; however, certain things can change the end behavior. You'll notice that in the attached graph, as x gets really really small, the function goes to negative infinity. As x gets very very big, the function goes to positive infinity.
Now, taking a look at your function, 2x^3 - x, things might change a little. Some things that change the end behavior of a graph include a negative coefficient for x^3, such as -x^3 or -5x^3. This would flip the graph over the y-axis, which would make the end behavior "swap", basically. Your function doesn't have a negative coefficient in front of x^3, so we're okay on that front, and it turns out your function has the same end behavior as the parent function, since no kind of reflection is occurring. I attached the graph of your function as well so you can see it, but what this means is that as x approaches infinity, or as x gets very big, your function also goes to infinity, and as x approaches negative infinity, or as x gets very small, your function goes to negative infinity.
Answer:
is the correct answer.
Step-by-step explanation:
We know that vertex equation of a parabola is given as:
where is the vertex of the parabola and
are the coordinate of points on parabola.
As per the question statement:
The parabola opens upwards that means coefficient of is positive.
Let
Minimum of parabola is at x = 3.
The vertex is at the minimum point of a parabola that opens upwards.
Putting value of a and h in the equation:
Formula used:
Comparing the equation formulated above with the options given we can observe that the equation formulated above is most similar to option A.
Comparing and
13 = 9+k
k = 4
Please refer to the graph attached.
Hence, correct option is
