What is the effect on the graph of the parent function f(x) = x when f(x) is replaced with f(x - 7)?

Mathematics

2 answers:

vfiekz [6]2 years ago

8 0

Answer:

B) Shifts the line 7 units down

Step-by-step explanation:

Translations are transformations that change the position of the graph of a function. The general form of the graph of a function is translated up, down, to the right, or to the left. The translations are considered rigid transformations.

You can check the answer simply by evaluating the function at x=0:

$f(0-7)=f(-7)=(-7)$

Also, I attached you the graph.

marin [14]2 years ago

7 0

Shifts the line 7 units down

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Write the limit as a definite integral on the interval [a, b], where ci is any point in the ith subinterval. Limit Interval lim

geniusboy [140]

Answer:

The corresponding definite integral may be written as

$\int_a^b \mathrm{(4x + 11)}\,\mathrm{d}x$

The answer of the above definite integral is

$\int_a^b \mathrm{(4x + 11)}\,\mathrm{d}x = 98$

Step-by-step explanation:

The given limit interval is

$\lim_{||\Delta|| \to 0} \sum\limits_{i=1}^n (4c_i + 11) \Delta x_i$

$[a, b] = [-8, 6]$

The corresponding definite integral may be written as

$\int_a^b \mathrm{(4x + 11)}\,\mathrm{d}x$

$\int_{-8}^6 \mathrm{(4x + 11)}\,\mathrm{d}x$

Bonus:

The definite integral may be solved as

$\int_{-8}^6 \mathrm{(4x + 11)}\,\mathrm{d}x \\\\\frac{4x^2}{2} + 11x \left \|{b=6} \atop {a=-8}} \right. \\\\2x^2 + 11x \left \|{b=6} \atop {a=-8}} \right. \\\\ 2(6^2 -(-8)^2 ) + 11(6 - (-8) \\\\2(36 - 64 ) + 11(6 + 8) \\\\2(-28 ) + 11(14) \\\\-56 +154 \\\\98$