help :(

Question

f(x)=|x²-10x+16|

- x intercept(s)?

- y intercepts(s)?

- domain and range?

- piecewise of function?

Answer 1

(a)

The expression is |x²-10x+16|.

Let us consider y = |x²-10x+16|

To calculate the x intercept, substitute y = 0.

|x²-10x+16| = 0

x²-10x+16 = 0

x²-8x -2x+16 = 0

x(x-8) -2(x-8) = 0

(x-8)(x-2) = 0

 x = 8, 2

Therefore x intercepts are x = 2 and x = 8.

Answer 2

(b)

The expression is |x²-10x+16|.

Let us consider y = |x²-10x+16|

To calculate the y intercept, substitute x = 0.

y = |0²-10*0+16|

y = |16|

y = 16

Therefore y intercept is y = 16.

Answer 3

(c)

The function is |x²-10x+16|.

Let us consider y = |x²-10x+16|

The domain of the function is the set of all real numbers.

Domain set is { x ∈ R : R}

The range of the function is positive value as the |x| = x and |-x| = x.

Then range of the function is greater than zero always.

Range set is{ y ∈ R : y ≥ 0}.

Answer 4

(d)

The function is |x²-10x+16|.

Let us consider y = |x²-10x+16|

a piecewise function is a function which is defined by multiple sub functions, each sub function applying to a certain interval of the main function's domain.

Now consider x²-10x+16 = 0

x²-10x+16 = 0

x²-8x -2x+16 = 0

x(x-8) -2(x-8) = 0

(x-8)(x-2) = 0

 x = 8, 2.

In the interval (-∞ , 2), the function is positive. Therefore y = x²-10x+16.

In the interval (2,8), the function is negative. Therefore y = -(x²-10x+16).

In the interval (8, +∞), the function is positive. Therefore y = x²-10x+16.

Therefore the function can be written as

The piece-wise function is