Find all holes of the function f(x) = $$\frac{x^2 + x - 6}{2x + 6}$$ . Write your answer as a coordinate point in simplest form. If no hole exists, write 'none'.

The hole is at the coordinate point (-3, $$-\frac{5}{3}$$ ).

The function f(x) = -2 $$\log_3 (x + 8)$$ is decreasing on its domain of x > -8.

The function f(x) = -2 $$\log_3 (x + 8)$$ decreases on its domain.

The end behavior on the left side of the function f(x) = $$-2 \log_3 (x + 8)$$ is y to infinity as x approaches -8.

The left end behavior of f(x) = $$-2 \log_3 (x + 8)$$ is y \to \infty.

The end behavior on the right side of the function f(x) = $$-2 \log_3 (x + 8)$$ is y to negative infinity as x approaches infinity.

The right end behavior of f(x) = $$-2 \log_3 (x + 8)$$ is y \to -\infty.

Solve for all values of x in the equation $$\log_{-2x-1}(2x^2 - 10x - 19) = 2.$$

Find the values of x that satisfy the equation.

Condense the logarithm $$d \log a - 3 \log c$$ into a single logarithm.

The condensed form is $$\log\left(\frac{a^d}{c^3}\right)$$ .

Expand the logarithm $$\log x^2 y^3$$ fully using the properties of logs.

The expanded form is $$2 \log x + 3 \log y$$ .

Express the final answer of $$\log x^2 y^3$$ in terms of $$\log x$$ and $$\log y$$ .

The final answer is $$2 \log x + 3 \log y$$ .

Express the final answer of $$\log 7x^4$$ in terms of $$\log x$$ .

The final answer is $$\log 7 + 4 \log x$$ .

The function f(x) = -2 $$\log_3 (x + 8)$$ is a decreasing function.

The function is decreasing on its domain.

The left end behavior of f(x) = $$-2 \log_3 (x + 8)$$ is y to infinity.

The left end behavior is y \to \infty.

The y-intercept represents a prediction of the number of hot cocoas sold when the temperature is 0°F.

y-intercept indicates the starting point of hot cocoa sales at 0°F.

A prediction of a student's quiz score if they spent 1 hour on their homework.

The expected quiz score based on homework time spent.

The number of times the cricket could be expected to chirp if it's 85°F.

The expected chirps per minute at 85°F.

After an oil spill in the ocean, oil continues to leak into the water.

Write a power regression equation for the data, rounding all coefficients to the nearest ten-thousandth.

Find the diameter of the oil spill, to the nearest meter, after 37 hours.

Use the power regression equation to calculate the diameter.

The orbital speeds of asteroids and their distance from the sun are related.

Write a power regression equation for the data, rounding all coefficients to the nearest thousandth.

The equation $$x^2 + y^2 + 8x + 6y + 0 = 0$$ represents a conic section.

Identify the type of conic represented by this equation.

The equation -9x^2 + 16y^2 - 90x - 160y + 31 = 0 represents which type of conic section?

This equation represents a hyperbola.

A parabola can be drawn given a focus of (8, 6) and a directrix of y = 2. Write the equation of the parabola.

The equation of the parabola is $$(x - 8)^2 = 8(y - 4)$$ .

A parabola can be drawn given a focus of (8, 3) and a directrix of x = 10. Write the equation of the parabola.

The equation of the parabola is $$(y - 3)^2 = -4(x - 9)$$ .

Write the absolute value function f(x) = $$|x^2 - 6x + 5|$$ as a piecewise function.

The piecewise function is: f(x) = $$\begin{cases} x^2 - 6x + 5, & \text{if } x^2 - 6x + 5 \geq 0 \\ -(x^2 - 6x + 5), & \text{if } x^2 - 6x + 5

Mathematical Functions and Simplifications Flashcards

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30 questions

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1.

FLASHCARD QUESTION

Front

Back

The domain is x>= 3.

2.

FLASHCARD QUESTION

Front

Back

The range is y >= -2.

3.

FLASHCARD QUESTION

Front

Back

The simplified form is 2x^4.

4.

FLASHCARD QUESTION

Front

Back

The solution is x = 6.

5.

FLASHCARD QUESTION

Front

Back

Vertical asymptotes occur where the denominator is zero: 2x - 8 = 0.

6.

FLASHCARD QUESTION

Front

Back

7.

FLASHCARD QUESTION

Front

Back

Since the degree of the denominator is greater, the horizontal asymptote is y = 0.

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