{"id":9746,"date":"2022-01-26T23:36:40","date_gmt":"2022-01-26T18:06:40","guid":{"rendered":"https:\/\/mathemerize.com\/?p=9746"},"modified":"2022-01-26T23:36:43","modified_gmt":"2022-01-26T18:06:43","slug":"exponential-function","status":"publish","type":"post","link":"https:\/\/mathemerize.com\/exponential-function\/","title":{"rendered":"Exponential Function – Graph, Formula, Domain and Range"},"content":{"rendered":"

Here you will learn what is exponential function graph, formula, domain and range.<\/p>\n

Let’s begin –<\/p>\n

Exponential Function Formula<\/h2>\n

Definition<\/strong> : If a is a positive real number other than unity, then a function that associates each x \\(\\in\\) R to \\(a^x\\) is called the exponential function.<\/p>\n

In other words, a function f : R \\(\\rightarrow\\) R defined by f(x) = \\(a^x\\), where a > 0 and a \\(\\ne\\) 1 is called the exponential function.<\/p>\n

Formula<\/strong> : It is defined by the formula f(x) = \\(a^x\\).<\/p>\n

where a > 0 and a \\(\\ne\\) 1<\/p>\n

a is a constant, which is the base of the function<\/p>\n

x is any variable.<\/p><\/blockquote>\n

Also Read<\/strong> : Types of Functions in Maths \u2013 Domain and Range<\/a><\/p>\n

Exponential Function Graph<\/h2>\n

Case 1<\/strong> : When a > 1,<\/p>\n

We observe that the values of y = f(x) = \\(a^x\\) increase as the value of x increase.<\/p>\n

Also,  f(x) = \\(\\begin{cases} < 1, & \\text{for}\\ x > 0 \\\\ = 1, & \\text{for}\\ x = 0 \\\\ > 1, & \\text{for}\\ x < 0 \\end{cases}\\).<\/p>\n

Thus, the graph f(x) = \\(a^x\\) for a > 1 is  :<\/p>\n

\"exponential<\/p>\n

Case 2<\/strong> : When 0 < a < 1<\/p>\n

In this case, the values of y = f(x) = \\(a^x\\) decrease with increase in x and y > 0 for all x \\(\\in\\) R.<\/p>\n

Also, f(x) = \\(\\begin{cases} > 1, & \\text{for}\\ x > 0 \\\\ = 1, & \\text{for}\\ x = 0 \\\\ < 1, & \\text{for}\\ x < 0 \\end{cases}\\).<\/p>\n

Thus, the graph f(x) = \\(a^x\\) for 0 < a < 1 is  :<\/p>\n

\"exponential<\/p>\n

Domain and Range<\/h2>\n

We observe that the domain of the exponential function is R the set of all real numbers and the range is the set \\((0, \\infty)\\) as it attains only positive values.<\/p>\n

Domain<\/strong> : R<\/p>\n

Range<\/strong> : \\((0, \\infty)\\)<\/p><\/blockquote>\n","protected":false},"excerpt":{"rendered":"

Here you will learn what is exponential function graph, formula, domain and range. Let’s begin – Exponential Function Formula Definition : If a is a positive real number other than unity, then a function that associates each x \\(\\in\\) R to \\(a^x\\) is called the exponential function. In other words, a function f : R …<\/p>\n

Exponential Function – Graph, Formula, Domain and Range<\/span> Read More »<\/a><\/p>\n","protected":false},"author":1,"featured_media":0,"comment_status":"open","ping_status":"open","sticky":false,"template":"","format":"standard","meta":{"site-sidebar-layout":"default","site-content-layout":"default","ast-global-header-display":"","ast-main-header-display":"","ast-hfb-above-header-display":"","ast-hfb-below-header-display":"","ast-hfb-mobile-header-display":"","site-post-title":"","ast-breadcrumbs-content":"","ast-featured-img":"","footer-sml-layout":"","theme-transparent-header-meta":"","adv-header-id-meta":"","stick-header-meta":"","header-above-stick-meta":"","header-main-stick-meta":"","header-below-stick-meta":""},"categories":[26],"tags":[808,809,807],"yoast_head":"\nExponential Function - Graph, Formula, Domain and Range<\/title>\n<meta name=\"description\" content=\"In this post you will learn what is exponential function graph and formula, domain and range of exponential function.\" \/>\n<meta name=\"robots\" content=\"index, follow, max-snippet:-1, max-image-preview:large, max-video-preview:-1\" \/>\n<link rel=\"canonical\" href=\"https:\/\/mathemerize.com\/exponential-function\/\" \/>\n<meta property=\"og:locale\" content=\"en_US\" \/>\n<meta property=\"og:type\" content=\"article\" \/>\n<meta property=\"og:title\" content=\"Exponential Function - 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