<h3>
Answer:</h3>
48 - Left
- a. domain: all real numbers; range: all numbers greater than or equal to zero
- b. x-intercept: x=0; y-intercept: y=0
- c. decreasing for x < 0; increasing for x > 0; constant for x=0
- d. even; the axis of symmetry is x=0
48 - Right
- a. both the domain and range are all real numbers
- b. x-intercept: x=0; y-intercept: y=0
- c. increasing everywhere except x=0; constant for x=0
- d. odd; symmetrical about the origin
<h3>
Step-by-step explanation:</h3>
48 - Left
a. The function is defined for all values of x, so its domain is all real numbers. (The <em>domain</em> is the set of numbers for which the function is defined.) For any x (positive or negative), both the graph and the function f(x)=x² tell you that the value of f(x) cannot be less than zero. Hence the range is all numbers greater than or equal to zero (all non-negative numbers). (The <em>range</em> is the set of values the function can produce.)
b. The only point where the function crosses either axis is the point (0, 0). This is both the x- and y-intercept.
c. The function goes "downhill" left of x=0, so is decreasing there. The function goes "uphill" right of x=0, so is increasing there. At x=0, the function is horizontal, so is constant there.
d. The left branch is a mirror image of the right branch, reflected across the vertical line x=0. That line is the axis of symmetry. Every point on the left branch is as far to the left of that line as the corresponding point on the right branch is to the right of it. When x=0 is the line of symmetry, the function is an even function.
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48 - Right
a. As with f(x) = x², the function f(x) = x³ is defined for all values of x. (This is true for <em>any polynomial function</em>.) Hence the domain is all real numbers.
Unlike f(x) = x², the function f(x) = x³ can produce any value of f(x), so the range is all real numbers.
b. As with f(x) = x², the only place where the graph crosses either axis is the point (0, 0). So, both the x- and y-intercept are 0.
c. The function goes "uphill" everywhere except at x=0, so is increasing for all x except x=0, where it is constant.
d. A polynomial of odd degree is an odd function, symmetrical about the origin. Every point above or to the right of the origin has a matching point below or to the left of the origin by the same distance.
