The equation (x^2/a^2) + (y^2/b^2) = 1 represents a family of ellipses with varying semi-major (a) and semi-minor (b) axes.

The equation y = a + b cos(x) represents cosine waves with varying amplitudes 'b' and vertical shifts 'a'.

The equation y = a e^(bx) represents a family of exponential functions with varying growth rates.

The equation y = a sin(bx + c) represents a family of trigonometric functions (sine waves) with varying amplitude (a) and frequency (b).

The equation y = a(x - h)^2 + k represents a family of parabolas with vertex at (h, k) and varying 'a' determining the direction and width.

The equation y = e^(kx) represents a family of exponential functions with varying growth rates (k).

The equation y = k/x represents a family of hyperbolas where k is a constant.

The equation y = kx^2 represents a family of parabolas that open upwards or downwards depending on the sign of 'k'.

The equation y = mx^3 + bx + c represents a family of cubic functions with varying coefficients.

The equation y = mx^3 + bx^2 + cx + d represents a family of cubic functions with varying coefficients.

The equation y = mx^3 + c represents a family of cubic functions where m is the coefficient of x^3.

Setting 2(1) + 1 = a and a = 2 for continuity.

Setting 2(3) + a = 5 gives a = -1.

Setting 4 = 2 gives a = 1 for continuity.

Setting the left limit (k(1) = k) equal to the right limit (1 + 1 = 2), we find k = 2.

Setting the left limit (3(2) + 1 = 7) equal to the right limit (2^2 - 1 = 3), we find m = 3.

All of these measures are affected by extreme values in the data set.

Interquartile Range is not affected by extreme values.

The discriminant for x^2 + 4x + 5 is negative (16 - 20 < 0), indicating no real roots.

An even function satisfies f(-x) = f(x). Here, f(x) = x^2 is even.

f(x) = x^2 - 4 is a polynomial function and is continuous everywhere, including at x = 2.

At x = 2, f(2) = 0 and limit from left is 0, limit from right is also 0. Hence, it is continuous.

To check continuity at x = 2, we find the left limit (4), right limit (4), and f(2) (4). All are equal, so f(x) is continuous.

f(x) = x^2 is a polynomial function and is continuous everywhere.

Check continuity and differentiability at x = 1 by equating left and right derivatives.

f(x) = x^2 is a polynomial and differentiable everywhere.

A function is even if f(-x) = f(x). Here, f(x) = x^2 is even.

h(x) = sqrt(x) is not a polynomial function.

g(x) = 1/x is not a polynomial because it has a negative exponent.

The function f(x) = 1/x is not defined at x = 0, hence it is not continuous there.