Abosulte value functions. Need HELP?

Question

Can somebody help me with these 2 problems. i need examples.
1. compare the function g(x) = Ix+cI, where c is any real number, with the function f(x) = IxI. Describe the axis of symmetry, the domain and the range of g.
2. compare the function h(x) = x + d, where d is any real number, with the function f(x) = IxI. Describe the axis of symmetry, the domain and the range of g.

the I___I is the absolute value

Answer 1

Number 1:
for g(x)
domain = where can values of x come from?
Here, there are no restrictions. x could be any real value.
(-inf., +inf.)

range: where the image will go (the value of the function). Because the entire function is inside the ABS sign, then it can only be positive. If c = -x (it seems to be allowed), the g(x) = 0.

So, we know it cannot be negative and we know it can go as low as 0, therefore the range is all non-negative values.
[0, +inf.)

Both f and g will look like a capital letter V, where the axis of symmetry is vertical and through the botton angle of the V. In f this is when x=0; in g, as we just saw, this is when x = -c.

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In number 2, you probably mean the range of h (not g).

h is a straight line, parallel to the right branch of f. If d=0, then h and f coincide for non-negative values of x.