Question

Which function has the given properties below? the domain is the set of all real numbers. one x-intercept is (startfraction pi over 2 endfraction, 0 endfraction). the maximum value is 3. the y-intercept is (0, –3). y = –3sin(x) y = –3cos(x) y = 3sin(x) y = 3cos(x)

Answer 1

The required function with maximum value 3 and x and y-intercepts π/2 and 3 respectively is y=-3cos(x)

What is a function?

A function is a rule that relates two variables.

Let us check the x-intercept, y-intercept, and maximum value for each function.

1)y =-3Sin(x)

for x-intercept put y=0

0 = -3Sin(x)

Sin(x) =0

x=0

for y-intercept put x=0

y=-3Sin0

y=0

The maximum value of the given function =the lower limit of the range of -3Sin(x) i.e. 3

Similarly, for y = -3cos(x)

x-intercept =π/2

y-intercept = 3

Maximum value of function = lower limit  of the range of  3cos(x) i.e. 3

Therefore, the required function with maximum value 3 and x and y-intercepts π/2 and 3 respectively is y=-3cos(x)

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