open-end question(f4)

[匿名]

2014-04-13 3:42 am

(1) compare the three functions y=3x+1 , y=x^2+3x+1 and y=3^x

(a) write down three differences and three similarities between the functions.
(b) You have attempted 4 quizzes in a school term. If y represents the score you
get in test x and x is the number from 1 to 4.which function would you prefer?
explain your answer.

(2) It is known that the quadratic graph y=x^2+bx+c passes through A(c,0),.......
Prove that the graph of the function is symmetric about the line is x=2.
The above 2 sentenses descibe a mathematics question.

(a) According to the given conditions, what properties does the function have?
wirte down at least 4 properties
(b) The words after (c,0) are covered by ink. Can you write down the given
conditions completely?

回答 (1)

用戶10012

2014-04-13 6:30 pm

✔ 最佳答案

(1)
Similarities :
(i) When x = 0, y = 1, that is they all pass through (0,1).
(ii) When x is very large ( tends to infinity), y is also very large ( also tends to infinity.)
(iii) For one value of x, there is only one corresponding value of y, since they are functions.
(2)
Differences :
(i) Slope of y = 3x + 1 and y = 3^x is always positive. Slope of y = x^2 + 3x + 1 can be +ve, -ve or zero.
(ii) Value of y of y = 3^x is always positive. y can be +ve or -ve for the other 2 functions.
(iii) y = x^2 + 3x + 1 is symmetrical about a vertical line ( x = - 3/2), the other two are not symmetrical.
(b)
I will chose y = 3x + 1, since score should be the same for every attempts.

2014-04-13 10:58:03 補充：
(2) If y = x^2 + bx + c, the line of symmetry is x = - b/2. If x = 2 is the line of symmetry , 2 = - b/2, then b = - 4. So the word after A(c,0) should be " and b = - 4". (a) 4 properties :(i) Symmetrical about x = 2. (ii) y - intercept is (0, c). (iii) Opening upwards. (iv) Vertex at (2, c - 4).

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