The funcilon f(x) = -(x + 5)(x +

1) is shown.
what is the range of the function?

all real numbers less than or equal to 4

all real numbers less than or equal to -3

all real numbers greater than or equal to 4

all real numbers greater than or equal to -3

all numbers less than or equal to .

Step-by-step explanation:

The original equation shown is in "root form", a form of a quadratic equation showing where it hits the -axis. This form does not show, like a "standard form" quadratic equation does, the vertex of the quadratic. The standard form equation is shown below.

If we want to solve this equation showing all our work, the best bet is converting our equation from root-form to standard-form, like so:

Based on the properties of a standard form equation I gave earlier, this equation will look like an upside down "U" with a maximum value of . Therefore (based on the italicized text above), the range of values for this equation must be "all real numbers less than or equal to ".

P.S: Message me with any questions or fixes I should make to my math.

ratios represent a pattern or relationship that can be scaled.

equivalent ratios are pairs of ratios that represent the same relationship between quantities, and can be generated by multiplying or dividing both quantities in the ratio by the same factor.

in this lesson, students will use double number lines and ratio reasoning to solve ratio problems. by partitioning double number lines into proportionate intervals, students will build an understanding of equivalent ratio relationships as those that are generated by multiplying or dividing two related quantities by the same number. this lesson will build upon students' prior understanding of multiplicative comparisons, number line reasoning and equivalent fractions (while highlighting the difference between equivalent fractions and equivalent ratios); and will build toward future work in this unit on building ratio tables, and work in future grades in proportionality, scaling, and expressing and graphing linear functions.

step-by-step explanation:

ratios represent a pattern or relationship that can be scaled.

equivalent ratios are pairs of ratios that represent the same relationship between quantities, and can be generated by multiplying or dividing both quantities in the ratio by the same factor.

in this lesson, students will use double number lines and ratio reasoning to solve ratio problems. by partitioning double number lines into proportionate intervals, students will build an understanding of equivalent ratio relationships as those that are generated by multiplying or dividing two related quantities by the same number. this lesson will build upon students' prior understanding of multiplicative comparisons, number line reasoning and equivalent fractions (while highlighting the difference between equivalent fractions and equivalent ratios); and will build toward future work in this unit on building ratio tables, and work in future grades in proportionality, scaling, and expressing and graphing linear functions.

think about the doctor who treated the major and the speaker in the short story "in another country." put yourself in the shoes of the doctor, and based on what you read in the story, write what you think his thoughts about the major and the speaker would be. use the following vocabulary in your response and change the form of these words as needed: detached resign withered