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Mathematics

Grade10

Easy

Question

How is the function $f left parenthesis x right parenthesis equals 2 to the power of x$ translated to obtain the graph of $g left parenthesis x right parenthesis equals 2 to the power of x plus 7 end exponent ?$

Shifts 7 units up
Shifts 7 units down
Shift 7 units left
Shift 7 units right

The correct answer is: Shift 7 units left

$g left parenthesis x right parenthesis equals f left parenthesis x plus 7 right parenthesis space c o m p a r e d space w i t h space g left parenthesis x right parenthesis equals f left parenthesis x minus h right parenthesis text Here end text h equals negative 7 less than 0 text So, the graph translates end text 7 text units left. end text$

Related Questions to study

Identify the parent function of the graph given below.

Identify the parent function of the graph given below.

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$text How is the function end text f left parenthesis x right parenthesis equals cube root of x space t r a n s l a t e d space t o space o b t a i n space t h e space g r a p h space o f space g left parenthesis x right parenthesis equals cube root of x minus 5 end root ?$

$text How is the function end text f left parenthesis x right parenthesis equals cube root of x space t r a n s l a t e d space t o space o b t a i n space t h e space g r a p h space o f space g left parenthesis x right parenthesis equals cube root of x minus 5 end root ?$

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$H o w space i s space t h e space f u n c t i o n space f left parenthesis x right parenthesis equals x squared space t r a n s l a t e d space t o space o b t a i n space t h e space g r a p h space o f space g left parenthesis x right parenthesis equals x squared plus 2 ?$

$H o w space i s space t h e space f u n c t i o n space f left parenthesis x right parenthesis equals x squared space t r a n s l a t e d space t o space o b t a i n space t h e space g r a p h space o f space g left parenthesis x right parenthesis equals x squared plus 2 ?$

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parallel

$text A businessman's monthly profit, in thousands of dollars, can be modelled by the function end text g left parenthesis x right parenthesis equals 2 x squared minus 5 x plus 3 text . Select the true statement. end text$

$text A businessman's monthly profit, in thousands of dollars, can be modelled by the function end text g left parenthesis x right parenthesis equals 2 x squared minus 5 x plus 3 text . Select the true statement. end text$

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$text The monthly sale of a new bike can be modelled by the function end text f left parenthesis x right parenthesis equals cube root of x minus 1 end root plus 4. text Select that is true about the feature of the function. end text$

$text The monthly sale of a new bike can be modelled by the function end text f left parenthesis x right parenthesis equals cube root of x minus 1 end root plus 4. text Select that is true about the feature of the function. end text$

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$text Find the maximum value of the function end text r left parenthesis x right parenthesis equals 2 minus square root of x plus 1 end root$

$text Find the maximum value of the function end text r left parenthesis x right parenthesis equals 2 minus square root of x plus 1 end root$

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parallel

$text Find the end text x text -intercept and end text y text -intercept of the function end text p left parenthesis x right parenthesis equals 1 minus 5 x text . end text$

$text Find the end text x text -intercept and end text y text -intercept of the function end text p left parenthesis x right parenthesis equals 1 minus 5 x text . end text$

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Identify the function that has a minimum value of 1.

Identify the function that has a minimum value of 1.

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Find the x-intercept of the function x² - 2.

Find the x-intercept of the function x² - 2.

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parallel

James started a small business. Over the days the profit is represented by the function $r left parenthesis x right parenthesis equals square root of x minus 5 end root plus 2$ .
Find the domain of the function r(x).

James started a small business. Over the days the profit is represented by the function $r left parenthesis x right parenthesis equals square root of x minus 5 end root plus 2$ .
Find the domain of the function r(x).

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James started a small business. Over the days the profit is represented by the function $r left parenthesis x right parenthesis equals square root of x minus 5 end root plus 2$ .
Find the minimum value of the function r(x).

James started a small business. Over the days the profit is represented by the function $r left parenthesis x right parenthesis equals square root of x minus 5 end root plus 2$ .
Find the minimum value of the function r(x).

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James started a small business. Over the days the profit is represented by the function $r left parenthesis x right parenthesis equals square root of x minus 5 end root plus 2$ .
Find the range of the function r(x).

James started a small business. Over the days the profit is represented by the function $r left parenthesis x right parenthesis equals square root of x minus 5 end root plus 2$ .
Find the range of the function r(x).

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parallel

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State the equation of the axis of symmetry for the given graph below.

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So, the equation of the axis of symmetry for the given graph is is x = -3.

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Therefore, for the given graph Domain is [-2, 2] and Range is [1, 5].

parallel

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