Archive for January, 2015

Problem 557

 

What is the range of 2x2 + 1.

 

Solution:-

 

The graph of the function is a parabola. The positive 2 in the equation will make the graph open up. The positive one shifts the graph up vertically. The range relates to they-values with respect to the graph. Therefore, the range is  y ≥ 1.

 

Problem 556

 

What is the range of the following function? 

f(x) = (4,6), (5,7),(6,8),(7,9)

 

Solution:-

 

Given a set of ordered pairs, the range is found by identifying the y-coordinates from the set.

 

 

So the range is {6, 7, 8, 9}.

Problem 555

Explain why there are restrictions on the domain for the function  f(x) = \frac{1}{x}.

 

Solution:-

 

The domain of a function is the set of values for which it is defined. For the given function x = 0 will cause the function to be undefined, since 1 divided by 0 is undefined. Therefore, the domain is the set of real numbers, except x = 0 or x ≠ 0..

 

Problem 554

 

Explain how a graph fails the vertical line test.

 

Solution:-

 

Any vertical line drawn through the graph cannot intersect the graph more than once. If any vertical line intersects more than once, the graph fails the vertical line test, and the graph is a relation. If any vertical line only intersects once, the graph passes the vertical line test, and the graph is a function.

 

Problem 553

 

 Explain why vertical lines have undefined slope.

 

Solution:-

 

When calculating the slope of a line, you find the change in y-coordinates divided by the change in x-coordinates. For a vertical line, the x-coordinates are constant with no change. Therefore, when you subtract their values, the difference is zero. In a fraction any number divided by zero is considered undefined. That means the slope of a vertical line is undefined.

 

Problem 552

Write the equation of the line with m = \frac{1}{7}   and b = \frac{3}{4}  ?

 

Solution:-

 

Substitute the values for slope and y-intercept into y = mx +b.

 

y = \frac{1}{7}x + \frac{3}{4}

Problem 551

 

Find the slope of the line through the points (5, 5) and (-5, 5).

 

Solution:-

 

Use the slope formula m = \frac{y_{2}-y_{1}}{x_{2}-x_{1}}

 

m = \frac{5- 5 }{-5-5}

 

m = 0

The slope is zero.

Problem 550

 

Find the slope of the line through the points (-1, 2) and (9, 7).

 

Solution:-

 

Use the slope formula m = \frac{y_{2}-y_{1}}{x_{2}-x_{1}}

 

m = \frac{7- 2 }{9- (-1)}

 

m =\frac{1}{2}

Problem 549

What is the slope of the line that is perpendicular to y = 4x – 3?

 

Solution:-

 

The slope is represented by m in y = mx + b. Perpendicular lines have opposite reciprocal slopes.

 

m = \frac{-1}{4}.

Problem 548

 

Which of the following graphs represents y = 3x + 3 ?

 

Solution:-

548

 

 

Look for the graph of a linear function with a slope of three and a y– intercept of three.