Question

1.What effect does replacing x with x−4 have on the graph for the function f(x) ?

Answer 1

Answer with explanation:

Ques 1)

We know that the transformation of the type:

          f(x) → f(x-k)

shifts the graph of the parent function f(x) k units to the right.

Hence, on  replacing x with x−4 the graph of the function f(x) will be shifted 4 units to the right.

The correct option is:

       The graph is shifted 4 units right.

Ques 2)

For finding the hole of a rational function we first factor the numerator and denominator of the function and then the roots of the factor which is common to both numerator and denominator is the hole of the graph.

Here we have a rational function as:

$f(x)=\dfracPx^2+3x-28}{x+7}$

which on factoring we get:

$f(x)=\dfrac{(x+7)(x-4)}{x+7}$

Hence, the common factor is: $x+7$

and the root of the factor is:  x= -7

Hence, the hole in the graph of function f(x) is:

                 x= -7

Ques 3)

We are given a function h(x) as:

h(x)=  {x  if  x≤ -1

    and -x if x> -1

The graph is a straight increasing line with positive slope in the interval (-∞,-1] and there is a closed circle at (-1,-1)

and also the graph is a straight decreasing line with negative slope in the interval (-1,∞) and there is a open circle at (-1,1).

The correct graph is attached to the answer.

Answer 2

Answer:

The absolute value wiill change

Step-by-step explanation:

Inserting different values in the absolute value can change the numerical value of the equation as a whole.