Without graphing, what are the vertex , axis of symmetry, and transformations of the parent function? Y - |8x-3| - 3

Given:

Consider the given function is

To find:

The vertex , axis of symmetry, and transformations of the parent function?

Solution:

We have,

     ...(i)

It is an absolute function.

The vertex form of an absolute function is

      ...(ii)

where, a is a constant, (h,k) is vertex and x=h is axis of symmetry.

From (i) and (ii), we get

So,

Parent function of an absolute function is

Since, a=8 therefore, parent function vertically stretched by factor 8.

, so the function shifts unit right.

k=-3<0, so the function shifts 3 units down.

Therefore, the vertex is and Axis of symmetry is . The parent function vertically stretched by factor 8, shifts unit right and  3 units down.

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step-by-step explanation:

answer: on graphs, the open and closed circles, or vertical asymptotes drawn as dashed lines us identify discontinuities.

as before, graphs and tables allow us to estimate at best.

when working with formulas, getting zero in the denominator indicates a point of discontinuity.

when working with piecewise-defined functions, check for discontinuities at the transition points where one piece ends and the next begins.

step-by-step explanation: