My question is on here : SparkNotes: SAT Subject Test: Math Level 2: Review Questions
#5. I don't get why and I don't get its explanations
Sorry for just pasting the website, I cannot copy the diagram. Thanks in advance!!
My question is on here : SparkNotes: SAT Subject Test: Math Level 2: Review Questions
#5. I don't get why and I don't get its explanations
Sorry for just pasting the website, I cannot copy the diagram. Thanks in advance!!
Hello, fabxx!
I don't get its explanations either . . .
5. A portion of the graph of $\displaystyle y = f(x)$ is shown.Code:| * | * * * * * | * * *| * - - - -*- - -*-+- - -*- - - - - * - - - * | * * | * |
Which of the following could be $\displaystyle f(x)$ ?
Note that the graph has four x-intercepts, two positive and two negative.
One of the x-intercepts is 0; this graph would contain the origin.$\displaystyle (A)\;x^4 + ax^3 + bx^2 + cx$ .No
This quartic opens down.$\displaystyle (C)\;-x^4+ax^3 + bx^2 + cx + d$ .No
This is a cubic function.$\displaystyle (D)\;x^3 + ax^2 + bx + c$ .No
To find the x-intercepts: .$\displaystyle x^4 + b^2x + c^2 \:=\:0$$\displaystyle (E)\;x^4+b^2x^2+c^2$ .No
Quadratic Formula: .$\displaystyle x^2 \;=\;\frac{-b^2 \pm\sqrt{b^4-4c^2}}{2}$
It can be shown that the right side is either negative or zero.
. . If it is negative, there are no real values of $\displaystyle x.$
. . If it is zero, there is only one x-intercept.
$\displaystyle (B)\;x^4+ax^2+b $ .Yes
To find the x-intercepts: .$\displaystyle x^4 + ax^2 + b \:=\:0$
Quadratic Formula: .$\displaystyle x^2 \;=\;\frac{-a \pm\sqrt{a^2-4b}}{2}$
If $\displaystyle a$ is negative, the right side is positive.
Hence, for $\displaystyle a < 0$, there are four x-intercepts:
. . $\displaystyle x \;=\;\pm\sqrt{\frac{-a \pm\sqrt{a^2-4n}}{2}} $
But the function in B is an even function while the graph is not that of an even function. So as written there is no answer.
Look at question #6. The given graph is not an odd function either.
That is just a poor set of problems and they are selling them as SAT review.