Question

1. for the graph of a function shown to the right, find (a) the domain and range, (b) the intercepts, if any, and (c) the zeros, if any. (a) the domain of the graph is \\( \boxed{} \\). (type your answer in interval notation.) the range of the graph is \\( \boxed{} \\). (type your answer in interval notation.) (b) find the x-intercept(s). select the correct choice below and, if necessary, fill in the answer box to complete your choice. \\( \bigcirc \\) a. the x-intercept(s) is/are \\( \boxed{} \\). (type an ordered pair. use a comma to separate answers as needed.) \\( \bigcirc \\) b. there is no x-intercept. find the y-intercept(s). select the correct choice below and, if necessary, fill in the answer box to complete your choice. \\( \bigcirc \\) a. the y-intercept(s) is/are \\( \boxed{} \\). (type an ordered pair. use a comma to separate answers as needed.) \\( \bigcirc \\) b. there is no y-intercept. (c) determine the zeros of the function, if any. select the correct choice below and, if necessary, fill in the answer box to complete your choice. \\( \bigcirc \\) a. the zero(s) of the function is/are \\( \boxed{} \\). (type an integer or a decimal. use a comma to separate answers as needed.) \\( \bigcirc \\) b. there is no zero of the function. 19. find the equation of the line that contains the given points. write the equation in slope-intercept form, if possible. \\( (2, 14) \\) and \\( (-1, -7) \\) select the correct choice below and, if necessary, fill in the answer box to complete your choice. (simplify your answer. use integers or fractions for any numbers in the equation.) \\( \bigcirc \\) a. the equation of the line cannot be written in slope-intercept form. the equation of the line is \\( \boxed{} \\). \\( \bigcirc \\) b. the equation of the line in slope-intercept form is \\( \boxed{} \\). 20. solve the system using elimination. \\( \

$$\begin{cases} 4x + 16y = 4 \\\\ 4x - 16y = 4 \\end{cases}$$

\\) select the correct choice below and fill in any answer boxes in your choice. \\( \bigcirc \\) a. the solution is \\( \boxed{} \\). (type an ordered pair.) \\( \bigcirc \\) b. there are infinitely many solutions. \\( \bigcirc \\) c. there is no solution.

Explanation:

Problem 19: Find the equation of the line containing (2,14) and (-1,7)

Step 1: Calculate the slope (m)

The slope formula is \( m = \frac{y_2 - y_1}{x_2 - x_1} \). Let \((x_1, y_1) = (2, 14)\) and \((x_2, y_2) = (-1, 7)\). Then \( m = \frac{7 - 14}{-1 - 2} = \frac{-7}{-3} = \frac{7}{3} \).

Step 2: Use point - slope form to find the equation

Point - slope form is \( y - y_1 = m(x - x_1) \). Using the point \((2, 14)\) and \( m=\frac{7}{3} \), we have \( y - 14=\frac{7}{3}(x - 2) \).
Expand the right - hand side: \( y-14=\frac{7}{3}x-\frac{14}{3} \).
Add 14 to both sides: \( y=\frac{7}{3}x-\frac{14}{3}+14 \). Since \( 14=\frac{42}{3} \), then \( y=\frac{7}{3}x-\frac{14}{3}+\frac{42}{3}=\frac{7}{3}x+\frac{28}{3} \).

Step 1: Add the two equations

Add the left - hand sides and the right - hand sides of the two equations: \((4x + 16y)+(4x-16y)=4 + 4\).
Simplify the left - hand side: \(4x+4x+16y - 16y=8x\), and the right - hand side is 8. So we get \(8x=8\).

Step 2: Solve for x

Divide both sides of the equation \(8x = 8\) by 8: \(x=\frac{8}{8}=1\).

Step 3: Substitute x = 1 into one of the original equations

Substitute \(x = 1\) into the first equation \(4x+16y = 4\). We have \(4(1)+16y=4\).
Simplify: \(4 + 16y=4\). Subtract 4 from both sides: \(16y=4 - 4=0\). Then \(y = 0\).

Answer:

B. The equation of the line in slope - intercept form is \( y = \frac{7}{3}x+\frac{28}{3} \)

Problem 20: Solve the system using elimination \(

$$\begin{cases}4x + 16y=4\\4x-16y = 4\end{cases}$$

\)