Determine the x-intercept points of the function h(x) = (x – 5)(x – 6).

The x-intercept occurs when h(x) = 0

∴ let                  0 = (x – 5)(x – 6)                [using the knowledge that for the  

                                                                      produc to be 0, one of terms  

                                                                      must be zero]

⇒                 x - 5 = 0       ;      x - 6 = 0       [solve for x in each case]

⇒                      x = 5        ;           x = 6

Check:

If we graph the line we can see whether the intercepts are truly (5, 0) and (6,0). As seen below in the Desmos graph, it is.

answer: 20

step-by-step explanation:

find the magnitude of the trig term  

csc

(

x

)

−

1

by taking the absolute value of the coefficient.

1

find the lower bound of the range.

tap for more

y

=

−

2

find the upper bound of the range.

tap for more

y

=

0

the range is  

y

≤

−

2

or  

y

≥

0

.

(

−

∞

,

−

2

]

∪

[

0

,

∞

)

{

y

|

y

≤

−

2

,

y

≥

0

}

step-by-step explanation: