0. Functions

Common Functions

0. Functions

Common Functions

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Multiple Choice

In the graph shown, identify the y–intercept & slope. Write the equation of this line in Slope-Intercept form.

$y=\frac23x+1$

$y=-\frac23x+1$

$y=-2x+1$

$y=x+2$

Verified step by step guidance

First, identify the y-intercept of the line on the graph. The y-intercept is the point where the line crosses the y-axis. In this graph, the line crosses the y-axis at y = 1.

Next, determine the slope of the line. The slope is calculated as the change in y divided by the change in x between two points on the line. Choose two points on the line, such as (0, 1) and (3, -1).

Calculate the slope using the formula: slope = (y2 - y1) / (x2 - x1). Substitute the chosen points into the formula: slope = (-1 - 1) / (3 - 0) = -2/3.

Now, write the equation of the line in slope-intercept form, which is y = mx + b, where m is the slope and b is the y-intercept. Substitute the slope and y-intercept into the equation: y = -2/3x + 1.

Verify the equation by checking if other points on the line satisfy the equation. For example, check if the point (3, -1) satisfies the equation: y = -2/3(3) + 1 = -2 + 1 = -1, which is correct.

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Textbook Question

[Technology Exercise]

a. Graph the functions f(x) = x/2 and g(x) = 1 + (4/x) together to identify the values of x for which

x/2 > 1 + 4/x

b. Confirm your findings in part (a) algebraically.

Textbook Question

[Technology Exercise]

a. Graph the functions f(x) = 3/(x − 1) and g(x) = 2/(x + 1) together to identify the values of x for which

3/(x − 1) < 2/(x + 1)

b. Confirm your findings in part (a) algebraically.

Textbook Question

Finding a Viewing Window

In Exercises 5–30, find an appropriate graphing software viewing window for the given function and use it to display that function’s graph. The window should give a picture of the overall behavior of the function. There is more than one choice, but incorrect choices can miss important aspects of the function.

f(x) = (x² − 1)/(x² + 1)

Textbook Question

Use graphing software to graph the functions specified in Exercises 31–36.

Select a viewing window that reveals the key features of the function.

Graph the upper branch of the hyperbola y² − 16x² = 1.

Multiple Choice

Identify the ordered pair of the vertex of the parabola. State whether it is a minimum or maximum.

Multiple Choice

Where is the axis of symmetry located on the given parabola?

Multiple Choice

Determine if the given function is a polynomial function. If so, write in standard form, then state the degree and leading coefficient. $f\left(x\right)=4x^3+\frac12x^{-1}-2x+1$

Multiple Choice

Determine if the given function is a polynomial function. If so, write in standard form, then state the degree and leading coefficient. $f\left(x\right)=2+x$

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