Answer to Question #156243 in Trigonometry for aasia tariq

Question

find the domain of the indicated functions.express answers in both interval notation and inequality notation.

f (x)=4-9x+3x²

translate each algebraic definition of the following function into a verbal definition.

f (x)=2x²⁺⁵

g (x)=-2x+7

M (x)=5t-2

Answer 1

1) f (x)=4-9x+3x² ;

This function can get all numbers for the domain:

$x\in (-\infin;\infin)$ ; $-\infin\le x\le \infin$ ;

2) f (x)=2x²+5 ;

This is a quadratic function. Its domain includes all real numbers. Its graph is a parabola. That graph does not intersect with the x-axis. Its range includes $[5,\infin)$ , where x=0;

3) g (x)=-2x+7

This is a linear function. Its domain and range include all real numbers. Its graph is a straight line. That graph intersects with coordinates on (3.5, 0) and (0,7). Its range includes $(-\infin,\infin)$ , where x=0;

4) M (x)=5t-2

This is a linear function. Its domain include all real numbers. Its graph is a line.